TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. \[\begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.830 \\ \text { R Square } & 0.689 \\ \text { Adjusted R Square } & 0.662 \\ \text { Standard Error } & 17501.643 \\ \text { Observations } & 26 \end{array} \end{array}\] ANOVA $\begin{array}{lcrrrr} \hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\ \hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text {Residual }& 23 & 7045072780 & 306307512 & & \\ \text {Total }& 25 & 22624849820 & & & \\ \hline \end{array}$ \[\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\ \hline \end{array}\] -Referring to Table 14-5, which of the independent variables in the model are significant at the 5% level?

A) Capital B) Capital, Wages C) Wages D) none of the above A) Capital B) Capital, Wages C) Wages D) none of the above

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ $\begin{array}{ll} \hline \text { Regression Statistics } \\ \hline \text { Multiple R }& 0.916 \\ \text { R Square} & 0.839 \\ \text { Adjusted R Square} & 0.732 \\ \text { Standard Error }& 0.24685 \\ \text { Observations} & 6 \\ \hline \end{array}$ ANOVA $\begin{array}{lccclc} \hline & \text {d f }& \text { SS }& \text { M S } & \text { F } & \text {Significance F } \\ \hline \text { Regression} & 2 & 0.95219 & 0.47610 & 7.813 & 0.0646 \\ \text {Residual} & 3 & 0.18281 & 0.06094 & & \\ \text {Total} & 5 & 1.13500 & & & \\ \hline \end{array}$ $\begin{array}{lrcrr} \hline & \text {Coefficients }& \text {Standard Error} & \text {t Stat } & \text { p -value} \\ \hline \text { Intercept }& 4.593897 & 1.13374542 & 4.052 & 0.0271 \\ \text {Units }& -0.247270 & 0.06268485 & -3.945 & 0.0290 \\ \text {SAT Total }& 0.001443 & 0.00101241 & 1.425 & 0.2494 \\ \hline \end{array}$ -Referring to Table 14-7, the department head wants to use a t test to test for the significance of the coefficient of X1. The value of the test statistic is_____ .

The answer of TABLE 14-7 The department head of the...

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT $\begin{array}{lc} {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adjusted R Square }& 0.976 \\ \text { Standard Error } & 0.299 \\ \text { Observations } & 10 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} \hline & \text { d f}& \text { SS } & \text {MS } & \text { F } & \text {Significance F } \\ \hline \text { Regression} & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text {Residual }& 7 & 0.6277 & 0.0897 & & \\ \text {Total} & 9 & 34.0440 & & & \\ \hline \end{array}$ $\begin{array}{lcccr} \hline & \text {Coefficients} & \text { Standard Error} & \text { t Stat }& \text { p -value} \\ \hline \text {Intercept }& -0.0861 & 0.5674 & -0.152 & 0.8837 \\ \text {GDP} & 0.7654 & 0.0574 & 13.340 & 0.0001 \\ \text {Price }& -0.0006 & 0.0028 & -0.219 & 0.8330 \\ \hline \end{array}$ -Referring to Table 14-3, to test whether aggregate price index has a positive impact on consumption, the p-value is

A) 0.4165. B) 0.5835. C) 0.8330. D) 0.0001. A) 0.4165. B) 0.5835. C) 0.8330. D) 0.0001.

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: Regression Analysis $\begin{array}{lr} \hline\text {Regression Statistics } \\ \hline\text { Multiple R} & 0.63 \\ \text {R Square }& 0.40 \\ \text {Adjusted R Square} & 0.23 \\ \text {Standard Error }& 50.00 \\ \text {Observations} & 15.00 \\ \hline \end{array}$ ANOVA $\begin{array}{lccccc} \hline & \text { d f} & \text {SS} & \text {MS} & \text {F } & \text {Significance F } \\ \hline \text {Regression} & 3 & & 5994.24 & 2.40 & 0.12 \\ \text {Residual }& 11 & 27496.82 & & & \\ \text {Total }& 45479.54 & & & \\ \hline \end{array}$ $\begin{array}{lccrrrr} \hline & \text {oefficients}&\text { Standard Error }& \text { t Stat} &\text { p-value }& \text {Lower 99.0\% }& \text {Upper 99.0 \% } \\ \hline\text { Intercept} & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\ \text {AGE }& -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\ \text {TICKETS}& 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\ \text {DENSITY} & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\ \hline \end{array}$ -Referring to Table 14-10, the residual mean squares (MSE) that are missing in the ANOVA table should be ______.

The answer of TABLE 14-10 You worked as...

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: $\begin{array}{ll} & \text { Regression Stuistics } \\ \hline \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } &50 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} \hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\ \hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\ \text {Residual} & & 1214.2264 & 26.3962 & \\ Total & 49 & 4820.0000 & & & \\ \hline \end{array}$ $\begin{array}{lcccc} \hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\ \hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\ \hline \end{array}$ -Referring to Table 14-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, he obtained an r2 value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

A) 51.8% B) 72.6% C) 2.8% D) 74.8% A) 51.8% B) 72.6% C) 2.8% D) 74.8%

TABLE 14-17 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: $\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\ \text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\ \text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests $ \begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array} $ -Referring to Table 14-17, what is the p-value of the test statistic when testing whether Income makes a significant contribution to the model in the presence of the other independent variables?

The answer of TABLE 14-17 The marketing manager for...

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, XS1U1B11S1U1B0S1U1B1 S1U1B0= % Attendance, XS1U1B12S1U1B0S1U1B1 S1U1B0= Salaries and XS1U1B13 S1U1B0= Spending: $\begin{array}{lr} \hline\text {Regression Statistics } \\ \hline \text {Multiple R }& 0.7930 \\ \text {R Square} & 0.6288 \\ \text {Adjusted R Square} & 0.6029 \\ \text {Standard Error }& 10.4570 \\ \text {Observations }& 47 \\ \hline \end{array}$ ANOVA $\begin{array}{lccccc} \hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\ \hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\ \text { Residual} & 43 & 4702.02 & 109.35 & & \\ \text { Total }& 46 & 12667.11 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrr} \hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\ \hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\ \%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\ \text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\ \text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\ \hline \end{array}$ -Referring to Table 14-16, which of the following is the correct null hypothesis to test whether daily average of the percentage of students attending class has any effect on percentage of students passing the proficiency test?

A) $ H_{0}: \beta_{1}=0 $ B) $ H_{0}: \beta_{3}=0 $ C) $ H_{0}: \beta_{0}=0 $ D) $ H_{0}: \beta_{2}=0 $ A) $ H_{0}: \beta_{1}=0 $ B) $ H_{0}: \beta_{3}=0 $ C) $ H_{0}: \beta_{0}=0 $ D) $ H_{0}: \beta_{2}=0 $

TABLE 14-11 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on average total Scholastic Aptitude Test score (SAT) at the university or college, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: Logistic Regression Table $\begin{array}{lrrrrrrr} & & & && \text { Odds } & \text { 95: CI } \\ \text { Predictor } & {\text { Coef }} & \text { SE Coef } & Z &{\text { P }} & \text { Ratio } & \text { Lower } & \text { Upper } \\ \text { Constant } &-27.118&6 .696& -4.05 & 0.000 & & & \\ \text { SAT } & 0.015 & 0.004666 & 3.17 & 0.002 & 1.01 & 1.01 & 1.02 \\ \text { Toefl550 } & -0.390 & 0.9538 & -0.41 & 0.682 & 0.68 & 0.10 & 4.39 \\ \text { Room/Brd } & 2.078 & 0.5076 & 4.09 & 0.000 & 7.99 & 2.95 & 21.60 \end{array}$ Log-Likelihood = -21.883 Test that all slopes are zero: G = 62.083, DF = 3, P-Value = 0.000 Goodness-of-Fit Tests $ \begin{array}{lrcr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 143.551 & 76 & 0.000 \\ \text { Deviance } & 43.767 & 76 & 0.999 \\ \text { Hosmer-Lemeshow } & 15.731 & 8 & 0.046\end{array} $ TABLE 14-10 Regression Analysis $\begin{array}{lr} \hline\text {Regression Statistics } \\ \hline\text { Multiple R} & 0.63 \\ \text {R Square }& 0.40 \\ \text {Adjusted R Square} & 0.23 \\ \text {Standard Error }& 50.00 \\ \text {Observations} & 15.00 \\ \hline \end{array}$ ANOVA $\begin{array}{lccccc} \hline & \text { d f} & \text {SS} & \text {MS} & \text {F } & \text {Significance F } \\ \hline \text {Regression} & 3 & & 5994.24 & 2.40 & 0.12 \\ \text {Residual }& 11 & 27496.82 & & & \\ \text {Total }& 45479.54 & & & \\ \hline \end{array}$ $\begin{array}{lccrrrr} \hline & \text {oefficients}&\text { Standard Error }& \text { t Stat} &\text { p-value }& \text {Lower 99.0\% }& \text {Upper 99.0 \% } \\ \hline\text { Intercept} & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\ \text {AGE }& -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\ \text {TICKETS}& 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\ \text {DENSITY} & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\ \hline \end{array}$ -Referring to Table 14-11, what is the estimated probability that a school with an average SAT score of 1250, a TOEFL criterion that is at least 550, and the room and board expense of 5 thousand dollars will be a private school?

The answer of TABLE 14-11 A logistic regression model was...

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. \[\begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.830 \\ \text { R Square } & 0.689 \\ \text { Adjusted R Square } & 0.662 \\ \text { Standard Error } & 17501.643 \\ \text { Observations } & 26 \end{array} \end{array}\] ANOVA $\begin{array}{lcrrrr} \hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\ \hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text {Residual }& 23 & 7045072780 & 306307512 & & \\ \text {Total }& 25 & 22624849820 & & & \\ \hline \end{array}$ \[\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\ \hline \end{array}\] -Referring to Table 14-5, what is the p-value for testing whether Capital has a negative influence on corporate sales?

A) 0.05 B) 0.7258 C) 0.2743 D) 0.5485 A) 0.05 B) 0.7258 C) 0.2743 D) 0.5485

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, XS1U1B11S1U1B0S1U1B1 S1U1B0= % Attendance, XS1U1B12S1U1B0S1U1B1 S1U1B0= Salaries and XS1U1B13 S1U1B0= Spending: $\begin{array}{lr} \hline\text {Regression Statistics } \\ \hline \text {Multiple R }& 0.7930 \\ \text {R Square} & 0.6288 \\ \text {Adjusted R Square} & 0.6029 \\ \text {Standard Error }& 10.4570 \\ \text {Observations }& 47 \\ \hline \end{array}$ ANOVA $\begin{array}{lccccc} \hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\ \hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\ \text { Residual} & 43 & 4702.02 & 109.35 & & \\ \text { Total }& 46 & 12667.11 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrr} \hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\ \hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\ \%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\ \text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\ \text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\ \hline \end{array}$ -Referring to Table 14-16, which of the following is a correct statement?

A) The daily average of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1% holding constant the effects of all the remaining independent variables. B) The average percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of the percentage of students attending class increases by 1% holding constant the effects of all the remaining independent variables. C) The average percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of percentage of students attending class increases by 1%. D) The daily average of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1%. A) The daily average of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1% holding constant the effects of all the remaining independent variables. B) The average percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of the percentage of students attending class increases by 1% holding constant the effects of all the remaining independent variables. C) The average percentage of students passing the proficiency test is estimated to go up by 8.50% when daily average of percentage of students attending class increases by 1%. D) The daily average of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1%.

TABLE 14-17 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: $\begin{array}{lccccccrr} & & & & \text { Odds } & \text { 95 \% CI } \\ \text {Predictor }& \text {Coef }&\text { SE Coef }&\text { Z }& \text {P} &\text { Ratio} &\text { Lower} & \text {Upper }\\ \text {Constant }& -70.49 & 47.22 & -1.49 & 0.135 & & & \\ \text {Income }& 0.2868 & 0.1523 & 1.88 & 0.060 & 1.33 & 0.99 & 1.80 \\ \text {Lawn Size} & 1.0647 & 0.7472 & 1.42 & 0.154 & 2.90 & 0.67 & 12.54 \\ \text {Attitude} & -12.744 & 9.455 & -1.35 & 0.178 & 0.00 & 0.00 & 326.06 \\ \text {Teenager} & -0.200 & 1.061 & -0.19 & 0.850 & 0.82 & 0.10 & 6.56 \\ \text {Age} & 1.0792 & 0.8783 & 1.23 & 0.219 & 2.94 & 0.53 & 16.45 \end{array}$ Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests $ \begin{array}{lrrr}\text { Method } & \text { Chi-Square } & \text { DF } & \text { P } \\ \text { Pearson } & 9.313 & 24 & 0.997 \\ \text { Deviance } & 9.780 & 24 & 0.995 \\ \text { Hosmer-Lemeshow } & 0.571 & 8 & 1.000\end{array} $ -Referring to Table 14-17, what is the p-value of the test statistic when testing whether the model is a good-fitting model?

The answer of TABLE 14-17 The marketing manager for...

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, XS1U1B11S1U1B0S1U1B1 S1U1B0= % Attendance, XS1U1B12S1U1B0S1U1B1 S1U1B0= Salaries and XS1U1B13 S1U1B0= Spending: $\begin{array}{lr} \hline\text {Regression Statistics } \\ \hline \text {Multiple R }& 0.7930 \\ \text {R Square} & 0.6288 \\ \text {Adjusted R Square} & 0.6029 \\ \text {Standard Error }& 10.4570 \\ \text {Observations }& 47 \\ \hline \end{array}$ ANOVA $\begin{array}{lccccc} \hline &\text { d f } &\text { SS }& \text { MS }& \text { F } & \text { Significance F} \\ \hline \text { Regression }& 3 & 7965.08 & 2655.03 & 24.2802 & 2.3853 \mathrm{E}-09 \\ \text { Residual} & 43 & 4702.02 & 109.35 & & \\ \text { Total }& 46 & 12667.11 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrr} \hline &\text { Coeffs} & \text { Stnd Err} &\text { t Stat} &\text { p -value }&\text { Lower 95\%} \text { Upper 95\%} \\ \hline\text { Intercept }& -753.4225 & 101.1149 & -7.4511 & 2.88 \mathrm{E}-09 & -957.3401 & -549.5050 \\ \%\text { Attend }& 8.5014 & 1.0771 & 7.8929 & 6.73 \mathrm{E}-10 & 6.3292 & 10.6735 \\ \text { Salary} & 6.85 \mathrm{E}-07 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\ \text { Spending }& 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\ \hline \end{array}$ -Referring to Table 14-16, what is the p-value of the test statistic when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

The answer of TABLE 14-16 The superintendent of a...

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. \[\begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l r } \hline \text { Multiple R } & 0.830 \\ \text { R Square } & 0.689 \\ \text { Adjusted R Square } & 0.662 \\ \text { Standard Error } & 17501.643 \\ \text { Observations } & 26 \end{array} \end{array}\] ANOVA $\begin{array}{lcrrrr} \hline & \text { d f }&\text { S S } & \text { M S } & \text { F }&\text { Significance F } \\ \hline \text {Regression} & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text {Residual }& 23 & 7045072780 & 306307512 & & \\ \text {Total }& 25 & 22624849820 & & & \\ \hline \end{array}$ \[\begin{array} { l c c c c } & \text { Coefficients } & \text { Standard Error} & \text { t Stat } & \text { p-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { C apital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { W ages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \\ \hline \end{array}\] -Referring to Table 14-5, what is the p-value for Capital?

A) 0.01 B) 0.05 C) 0.025 D) none of the above A) 0.01 B) 0.05 C) 0.025 D) none of the above

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: Regression Analysis $\begin{array}{lr} \hline\text {Regression Statistics } \\ \hline\text { Multiple R} & 0.63 \\ \text {R Square }& 0.40 \\ \text {Adjusted R Square} & 0.23 \\ \text {Standard Error }& 50.00 \\ \text {Observations} & 15.00 \\ \hline \end{array}$ ANOVA $\begin{array}{lccccc} \hline & \text { d f} & \text {SS} & \text {MS} & \text {F } & \text {Significance F } \\ \hline \text {Regression} & 3 & & 5994.24 & 2.40 & 0.12 \\ \text {Residual }& 11 & 27496.82 & & & \\ \text {Total }& 45479.54 & & & \\ \hline \end{array}$ $\begin{array}{lccrrrr} \hline & \text {oefficients}&\text { Standard Error }& \text { t Stat} &\text { p-value }& \text {Lower 99.0\% }& \text {Upper 99.0 \% } \\ \hline\text { Intercept} & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\ \text {AGE }& -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\ \text {TICKETS}& 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\ \text {DENSITY} & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\ \hline \end{array}$ -Referring to Table 14-10, the standard error of the estimate is_____ .

The answer of TABLE 14-10 You worked as an intern at...

Exam 14: Introduction to Multiple Regression

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA d f S S M S F Significance F Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coefficients Standard Error t Stat p-value Intercept 15800.0000 6038.2999 2.617 0.0154 C apital 0.1245 0.2045 0.609 0.5485 W ages 7.0762 1.4729 4.804 0.0001 -Referring to Table 14-5, which of the independent variables in the model are significant at the 5% level?

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Question 121

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ Regression Statistics Multiple R 0.916 R Square 0.839 Adjusted R Square 0.732 Standard Error 0.24685 Observations 6 ANOVA d f SS M S F Significance F Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coefficients Standard Error t Stat p -value Intercept 4.593897 1.13374542 4.052 0.0271 Units -0.247270 0.06268485 -3.945 0.0290 SAT Total 0.001443 0.00101241 1.425 0.2494 -Referring to Table 14-7, the department head wants to use a t test to test for the significance of the coefficient of X1. The value of the test statistic is_____ .

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Question 122

A regression had the following results: SST = 82.55, SSE = 29.85. It can be said that 73.4% of the variation in the dependent variable is explained by the independent variables in the regression.

(True/False)

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Question 123

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA d f SS MS F Significance F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coefficients Standard Error t Stat p -value Intercept -0.0861 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 -Referring to Table 14-3, to test whether aggregate price index has a positive impact on consumption, the p-value is

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Question 124

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: Regression Analysis Regression Statistics Multiple R 0.63 R Square 0.40 Adjusted R Square 0.23 Standard Error 50.00 Observations 15.00 ANOVA d f SS MS F Significance F Regression 3 5994.24 2.40 0.12 Residual 11 27496.82 Total 45479.54 oefficients Standard Error t Stat p-value Lower 99.0\% Upper 99.0 \% Intercept 123.80 48.71 2.54 0.03 -27.47 275.07 AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Table 14-10, the residual mean squares (MSE) that are missing in the ANOVA table should be ______.

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Question 125

TABLE 14-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: Regression Stuistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA d f S S M S F Significance F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coefficients Standard Error t Stat p -value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 -Referring to Table 14-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, he obtained an r² value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

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Question 126

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one dollar increase in instructional spending per pupil on average percentage of students passing the proficiency test?

(Short Answer)

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Question 127

TABLE 14-17 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: Odds 95 \% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 Lawn Size 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-17, what is the p-value of the test statistic when testing whether Income makes a significant contribution to the model in the presence of the other independent variables?

(Short Answer)

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Question 128

The coefficient of multiple determination measures the fraction of the total variation in the dependent variable that is explained by the regression plane.

(True/False)

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Question 129

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, which of the following is the correct null hypothesis to test whether daily average of the percentage of students attending class has any effect on percentage of students passing the proficiency test?

(Multiple Choice)

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Question 130

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, the alternative hypothesis H1 : At least one of þj × 0 for j = 1, 2, 3 implies that percentage of students passing the proficiency test is related to all of the explanatory variables.

(True/False)

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Question 131

TABLE 14-11 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on average total Scholastic Aptitude Test score (SAT) at the university or college, the room and board expense measured in thousands of dollars (Room/Brd), and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise). The Minitab output is given below: Logistic Regression Table Odds 95: CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -27.118 6.696 -4.05 0.000 SAT 0.015 0.004666 3.17 0.002 1.01 1.01 1.02 Toefl550 -0.390 0.9538 -0.41 0.682 0.68 0.10 4.39 Room/Brd 2.078 0.5076 4.09 0.000 7.99 2.95 21.60 Log-Likelihood = -21.883 Test that all slopes are zero: G = 62.083, DF = 3, P-Value = 0.000 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 143.551 76 0.000 Deviance 43.767 76 0.999 Hosmer-Lemeshow 15.731 8 0.046 TABLE 14-10 Regression Analysis Regression Statistics Multiple R 0.63 R Square 0.40 Adjusted R Square 0.23 Standard Error 50.00 Observations 15.00 ANOVA d f SS MS F Significance F Regression 3 5994.24 2.40 0.12 Residual 11 27496.82 Total 45479.54 oefficients Standard Error t Stat p-value Lower 99.0\% Upper 99.0 \% Intercept 123.80 48.71 2.54 0.03 -27.47 275.07 AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Table 14-11, what is the estimated probability that a school with an average SAT score of 1250, a TOEFL criterion that is at least 550, and the room and board expense of 5 thousand dollars will be a private school?

(Short Answer)

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Question 132

A regression had the following results: SST = 82.55, SSE = 29.85. It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

(True/False)

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Question 133

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA d f S S M S F Significance F Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coefficients Standard Error t Stat p-value Intercept 15800.0000 6038.2999 2.617 0.0154 C apital 0.1245 0.2045 0.609 0.5485 W ages 7.0762 1.4729 4.804 0.0001 -Referring to Table 14-5, what is the p-value for testing whether Capital has a negative influence on corporate sales?

(Multiple Choice)

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Question 134

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 4 variables: age (X₁= Age), experience in the field (X₂= Exper), number of degrees (X₃= Degrees), and number of previous jobs in the field (X₄= Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: $\text {SUMMARY OUTPUT}$ Regression Statistics Multiple R 0.992 R Square 0.984 Adjusted R Square 0.979 Standard Error 2.26743 Observations 20 ANOVA d f SS M S F Significance F Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coefficients Standard Error t Stat p -value Intercept -9.611198 2.77988638 -3.457 0.0035 Age 1.327695 0.11491930 11.553 0.0001 Exper -0.106705 0.14265559 -0.748 0.4660 Degrees 7.311332 0.80324187 9.102 0.0001 Prevjobs -0.504168 0.44771573 -1.126 0.2778 -Referring to Table 14-8, the value of the coefficient of multiple determination, r² Y.1234, is____

(Short Answer)

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Question 135

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, which of the following is a correct statement?

(Multiple Choice)

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Question 136

TABLE 14-17 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0) and 15 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars), lawn size (Lawn Size, in thousands of square feet), attitude toward outdoor recreational activities (Attitude 0 = unfavorable, 1 = favorable), number of teenagers in the household (Teenager), and age of the head of the household (Age). The Minitab output is given below: Odds 95 \% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -70.49 47.22 -1.49 0.135 Income 0.2868 0.1523 1.88 0.060 1.33 0.99 1.80 Lawn Size 1.0647 0.7472 1.42 0.154 2.90 0.67 12.54 Attitude -12.744 9.455 -1.35 0.178 0.00 0.00 326.06 Teenager -0.200 1.061 -0.19 0.850 0.82 0.10 6.56 Age 1.0792 0.8783 1.23 0.219 2.94 0.53 16.45 Log-Likelihood = -4.890 Test that all slopes are zero: G = 31.808, DF = 5, P-Value = 0.000 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 9.313 24 0.997 Deviance 9.780 24 0.995 Hosmer-Lemeshow 0.571 8 1.000 -Referring to Table 14-17, what is the p-value of the test statistic when testing whether the model is a good-fitting model?

(Short Answer)

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Question 137

TABLE 14-16 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁= % Attendance, X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R Square 0.6029 Standard Error 10.4570 Observations 47 ANOVA d f SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 2.3853-09 Residual 43 4702.02 109.35 Total 46 12667.11 Coeffs Stnd Err t Stat p -value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 2.88-09 -957.3401 -549.5050 \% Attend 8.5014 1.0771 7.8929 6.73-10 6.3292 10.6735 Salary 6.85-07 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Table 14-16, what is the p-value of the test statistic when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

(Short Answer)

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Question 138

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression. Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA d f S S M S F Significance F Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coefficients Standard Error t Stat p-value Intercept 15800.0000 6038.2999 2.617 0.0154 C apital 0.1245 0.2045 0.609 0.5485 W ages 7.0762 1.4729 4.804 0.0001 -Referring to Table 14-5, what is the p-value for Capital?

(Multiple Choice)

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Question 139

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives. You performed a regression analysis in EXCEL and obtained the following information: Regression Analysis Regression Statistics Multiple R 0.63 R Square 0.40 Adjusted R Square 0.23 Standard Error 50.00 Observations 15.00 ANOVA d f SS MS F Significance F Regression 3 5994.24 2.40 0.12 Residual 11 27496.82 Total 45479.54 oefficients Standard Error t Stat p-value Lower 99.0\% Upper 99.0 \% Intercept 123.80 48.71 2.54 0.03 -27.47 275.07 AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Table 14-10, the standard error of the estimate is_____ .

(Short Answer)

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Question 140

A regression had the following results: SST = 82.55, SSE = 29.85. It can be said that 73.4% of the variation in the dependent variable is explained by the independent variables in the regression.

The coefficient of multiple determination measures the fraction of the total variation in the dependent variable that is explained by the regression plane.

A regression had the following results: SST = 82.55, SSE = 29.85. It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions and Sampling

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Two-Sample Tests

Analysis of Variance

Chi-Square Tests and Nonparametric Tests

Simple Linear Regression

Multiple Regression Model Building

Time-Series Forecasting and Index Numbers

Decision Making

Statistical Applications in Quality Management

Statistical Analysis Scenarios and Distributions

Filters