A statistics professor investigated some of the factors that affect an individual student's final grade in his or her course. He proposed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = final mark (out of 100). $x _ { 1 }$ = number of lectures skipped. $x _ { 2 }$ = number of late assignments. $x _ { 3 }$ = mid-term test mark (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below. THE REGRESSION EQUATION IS ŷ = \[41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }\] \[\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\ \hline \text { Constant } & 41.6 & 17.8 & 2.337 \\ x _ { 1 } & - 3.18 & 1.66 & - 1.916 \\ x _ { 2 } & - 1.17 & 1.13 & - 1.035 \\ x _ { 3 } & 0.63 & 0.13 & 4.846 \\ \hline \end{array}\] se = 13.74, R2 = 30.0%. \[\begin{array}{l} \text { ANALYSIS OF VARIANCE }\\ \begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\ \hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \\ \text { Error } & 46 & 8688 & 188.870 & \\ \hline \text { Total } & 49 & 12404 & & \\ \hline \end{array} \end{array}\] Do these data provide enough evidence at the 1% significance level to conclude that the final mark and the mid-term mark are positively linearly related?

@#IMG-DLM& . HA : @#IMG-DLM& 0. Rejection region:

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers impacts daily hot coffee sales revenue (in $00's). A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted. Excel output for a multiple linear regression is given below: \[\begin{array} { | c | c | r | } \hline \text { Coffee sales revenue } & \text { Temperature } & \text { Pastries/biscuits } \\ \hline 6.5 & 25 & 7 \\ \hline 10 & 17 & 13 \\ \hline 5.5 & 30 & 5 \\ \hline 4.5 & 35 & 6 \\ \hline 3.5 & 40 & 3 \\ \hline 28 & 9 & 15 \\ \hline \end{array}\] \(\begin{array}{|l|r|l|l|l|l|l|} \hline \text { SUMMARY OUTPUT } & & & & & & \\ \hline \text { Regression Statistios } & & & & & & \\ \hline \text { Multiple R } & 0.87 & & & & & \\ \hline \text { R Square } & 0.75 & & & & & \\ \hline \text { Adjusted R Square } & 0.59 & & & & & \\ \hline \text { Standard Error } & 5.95 & & & & & \\ \hline \text { Observations } & 6.00 & & & & & \\\hline \\ \hline \text { ANOVA } & & & & & \\ \hline & {d f} & SS & M S & F & \text { Significance } F \\ \hline \text { Regression } & 2.00 & 322.14 & 161.07 & 4.55 & 0.12 \\ \hline \text { Residual } & 3.00 & 106.20 & 35.40 & & \\ \hline \text { Total } & 5.00 & 428.33 & & & \\\hline \\ \hline & \text { Coeffients } & \text { Standard Error } & \text { tStat } & \text { P-value } & {\text { Lower } 95 \%} & {\text { Upper } 95 \%} \\ \hline \text { Intercept } & 18.68 & 37.88 & 0.49 & 0.66 & -101.88 & 139.24 \\ \hline \text { Temperature } & -0.50 & 0.83 & -0.60 & 0.59 & -3.15 & 2.15 \\ \hline \text { Pastries/biscuits } & 0.49 & 2.02 & 0.24 & 0.82 & -5.94 & 6.92 \\ \hline \end{array}\) Test the significance of the overall regression model, at α of 5%.

Ho: β1 = β2 = 0 HA: β1 ≠ 0 and

For the estimated multiple regression model ŷ = 30 F1F1F1S1F1F1F10 4x1 + 5x2 +3 x3, a one unit increase in x3, holding x1 and x2 constant, will result in which of the following changes in y?

A) y will increase by 3 units. B) y will increase by 2 units, estimated, on average. C) y will increase by 33 units D) y will increase by 3 units, estimated, on average. A) y will increase by 3 units. B) y will increase by 2 units, estimated, on average. C) y will increase by 33 units D) y will increase by 3 units, estimated, on average.

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week ( $x _ { 1 }$ ), the cholesterol level ( $x _ { 2 }$ ), and the number of points by which the individual's blood pressure exceeded the recommended value ( $x _ { 3 }$ ). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below: THE REGRESSION EQUATION IS ŷ = $55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$ \[\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\ \hline \text { Constant } & 55.8 & 11.8 & 4.729 \\ x _ { 1 } & 1.79 & 0.44 & 4.068 \\ x _ { 2 } & - 0.021 & 0.011 & - 1.909 \\ x _ { 3 } & - 0.016 & 0.014 & - 1.143 \\ \hline \end{array}\] se = 9.47 R2 = 22.5%. \[\begin{array}{l} \text { ANALYSIS OF VARIANCE }\\ \begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\ \hline \text { Regression } & 3 & 936 & 312 & 3.477 \\ \text { Error } & 36 & 3230 & 89.722 & \\ \hline \text { Total } & 39 & 4166 & & \\ \hline \end{array} \end{array}\] Is there enough evidence at the 10% significance level to infer that the model is useful in predicting length of life?

@#IMG-DLM& . HA : At least one @#IMG-DLM& is not e

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $x _ { 3 }$ = number of children under 10 years of age The computer output is shown below. THE REGRESSION EQUATION IS ŷ = $1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$ \[\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\ \hline \text { Constant } & 1.74 & 0.630 & 2.762 \\ x _ { 1 } & 0.091 & 0.025 & 3.640 \\ x _ { 2 } & 0.93 & 0.290 & 3.207 \\ x _ { 3 } & 0.26 & 0.180 & 1.444 \\ \hline \end{array}\] se = 2.06, R2 = 59.6%. \[\begin{array}{l} \text { ANALYSIS OF VARIANCE }\\ \begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\ \hline \text { Regression } & 3 & 288 & 96 & 22.647 \\ \text { Error } & 46 & 195 & 4.239 & \\ \hline \text { Total } & 49 & 483 & & \\ \hline \end{array} \end{array}\] Test at the 10% significance level to determine whether annual household income and annual family clothes expenditure are linearly related.

@#IMG-DLM& . HA : @#IMG-DLM& 0. Rejection region:

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $x _ { 3 }$ = number of children under 10 years of age The computer output is shown below. THE REGRESSION EQUATION IS ŷ = $1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$ \[\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\ \hline \text { Constant } & 1.74 & 0.630 & 2.762 \\ x _ { 1 } & 0.091 & 0.025 & 3.640 \\ x _ { 2 } & 0.93 & 0.290 & 3.207 \\ x _ { 3 } & 0.26 & 0.180 & 1.444 \\ \hline \end{array}\] se = 2.06, R2 = 59.6%. \[\begin{array}{l} \text { ANALYSIS OF VARIANCE }\\ \begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\ \hline \text { Regression } & 3 & 288 & 96 & 22.647 \\ \text { Error } & 46 & 195 & 4.239 & \\ \hline \text { Total } & 49 & 483 & & \\ \hline \end{array} \end{array}\] Test the overall model's validity at the 5% significance level.

@#IMG-DLM& . HA : At least one @#IMG-DLM& is not e

Exam 16: Multiple Regression

In regression analysis, the total variation in the dependent variable y, measured by $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }$ , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

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Question 21

Multicollinearity is a situation in which the independent variables are highly correlated with the dependent variable.

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Question 22

A statistics professor investigated some of the factors that affect an individual student's final grade in his or her course. He proposed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = final mark (out of 100). $x _ { 1 }$ = number of lectures skipped. $x _ { 2 }$ = number of late assignments. $x _ { 3 }$ = mid-term test mark (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below. THE REGRESSION EQUATION IS ŷ = $41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$ Predictor Coef StDev Constant 41.6 17.8 2.337 -3.18 1.66 -1.916 -1.17 1.13 -1.035 0.63 0.13 4.846 se = 13.74, R2 = 30.0%. ANALYSIS OF VARIANCE Source of Variation SS MS F Regression 3 3716 1238.667 6.558 Error 46 8688 188.870 Total 49 12404 Do these data provide enough evidence at the 1% significance level to conclude that the final mark and the mid-term mark are positively linearly related?

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Question 23

Test the hypotheses: $H _ { 0 } :$ There is no first-order autocorrelation HA : There is first-order autocorrelation, given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and $\alpha =$ 0.05.

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Question 24

A statistician wanted to determine whether the demographic variables of age, education and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = number of hours of television watched last week. $x _ { 1 }$ = age. $x _ { 2 }$ = number of years of education. $x _ { 3 }$ = income (in $1000s). The computer output is shown below. THE REGRESSION EQUATION IS ŷ = $22.3 + 0.41 x _ { 1 } - 0.29 x _ { 2 } - 0.12 x _ { 3 }$ Predictor Coef StDev Constant 22.3 10.7 2.084 0.41 0.19 2.158 -0.29 0.13 -2.231 -0.12 0.03 -4.00 se = 4.51 R2 = 34.8%. ANALYSIS OF VARIANCE Source of Variation SS MS F Regression 3 227 75.667 3.730 Error 21 426 20.286 Total 24 653 Interpret the coefficient $b _ { 2 }$ .

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Question 25

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers impacts daily hot coffee sales revenue (in $00's). A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted. Excel output for a multiple linear regression is given below: Coffee sales revenue Temperature Pastries/biscuits 6.5 25 7 10 17 13 5.5 30 5 4.5 35 6 3.5 40 3 28 9 15 SUMMARY OUTPUT Regression Statistios Multiple R 0.87 R Square 0.75 Adjusted R Square 0.59 Standard Error 5.95 Observations 6.00 ANOVA df SS MS F Significance F Regression 2.00 322.14 161.07 4.55 0.12 Residual 3.00 106.20 35.40 Total 5.00 428.33 Coeffients Standard Error tStat P-value Lower 95\% Upper 95\% Intercept 18.68 37.88 0.49 0.66 -101.88 139.24 Temperature -0.50 0.83 -0.60 0.59 -3.15 2.15 Pastries/biscuits 0.49 2.02 0.24 0.82 -5.94 6.92 Test the significance of the overall regression model, at α of 5%.

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Question 26

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) and number of different pastries and biscuits offered to customers impacts daily hot coffee sales revenue (in $00's). A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature and number of different pastries and biscuits offered on that day, noted. Describe the following scatterplots. Scatterplot of Daily hot coffee sales revenue vs Temperature Scatterplot of Daily hot coffee sales revenue Pastries/biscuits Residual scatterplot of Daily hot coffee sales revenue vs fitted values

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Question 27

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week ( $x _ { 1 }$ ), the cholesterol level ( $x _ { 2 }$ ), and the number of points by which the individual's blood pressure exceeded the recommended value ( $x _ { 3 }$ ). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below: THE REGRESSION EQUATION IS ŷ = $55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$ Predictor Coef StDev Constant 55.8 11.8 4.729 1.79 0.44 4.068 -0.021 0.011 -1.909 -0.016 0.014 -1.143 se = 9.47 R2 = 22.5%. ANALYSIS OF VARIANCE Source olf Variation df SS MS F Regression 3 936 312 3.477 Error 36 3230 89.722 Total 39 4166 Interpret the coefficient $b _ { 2 }$ .

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Question 28

For a multiple regression model:

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Question 29

For the estimated multiple regression model ŷ = 30  4x1 + 5x2 +3 x3, a one unit increase in x3, holding x1 and x2 constant, will result in which of the following changes in y?

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Question 30

An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week ( $x _ { 1 }$ ), the cholesterol level ( $x _ { 2 }$ ), and the number of points by which the individual's blood pressure exceeded the recommended value ( $x _ { 3 }$ ). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below: THE REGRESSION EQUATION IS ŷ = $55.8 + 1.79 x _ { 1 } - 0.021 x _ { 2 } - 0.016 x _ { 3 }$ Predictor Coef StDev Constant 55.8 11.8 4.729 1.79 0.44 4.068 -0.021 0.011 -1.909 -0.016 0.014 -1.143 se = 9.47 R2 = 22.5%. ANALYSIS OF VARIANCE Source of Variation SS MS F Regression 3 936 312 3.477 Error 36 3230 89.722 Total 39 4166 Is there enough evidence at the 10% significance level to infer that the model is useful in predicting length of life?

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Question 31

For a set of 30 data points, Excel has found the estimated multiple regression equation to be $\hat { y }$ = ?8.61 + 22x1 + 7x2 + 28x3, and has listed the t statistic for testing the significance of each regression coefficient. Using the 5% significance level for testing whether ?3 = 0, the critical region will be that the absolute value of the t statistic for ?3 is greater than or equal to:

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Question 32

In multiple regression, because of a commonly occurring problem called multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

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Question 33

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $x _ { 3 }$ = number of children under 10 years of age The computer output is shown below. THE REGRESSION EQUATION IS ŷ = $1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$ Predictor Coef StDev Constant 1.74 0.630 2.762 0.091 0.025 3.640 0.93 0.290 3.207 0.26 0.180 1.444 se = 2.06, R2 = 59.6%. ANALYSIS OF VARIANCE Source of Variation SS MS F Regression 3 288 96 22.647 Error 46 195 4.239 Total 49 483 Test at the 10% significance level to determine whether annual household income and annual family clothes expenditure are linearly related.

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Question 34

Which of the following is used to test the significance of the overall regression equation?

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Question 35

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $x _ { 3 }$ = number of children under 10 years of age The computer output is shown below. THE REGRESSION EQUATION IS ŷ = $1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$ Predictor Coef StDev Constant 1.74 0.630 2.762 0.091 0.025 3.640 0.93 0.290 3.207 0.26 0.180 1.444 se = 2.06, R2 = 59.6%.. ANALYSIS OF VARIANCE Source of Variation SS MS F Regression 3 288 96 22.647 Error 46 195 4.239 Total 49 483 Interpret the coefficient $\hat { \beta } _ { 2 }$ .

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Question 36

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ . Where: y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $x _ { 3 }$ = number of children under 10 years of age The computer output is shown below. THE REGRESSION EQUATION IS ŷ = $1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$ Predictor Coef StDev Constant 1.74 0.630 2.762 0.091 0.025 3.640 0.93 0.290 3.207 0.26 0.180 1.444 se = 2.06, R2 = 59.6%. ANALYSIS OF VARIANCE Source of Variation SS MS F Regression 3 288 96 22.647 Error 46 195 4.239 Total 49 483 Test the overall model's validity at the 5% significance level.

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Question 37

A multiple regression analysis that includes 4 independent variables results in a sum of squares for regression of 1200 and a sum of squares for error of 800. The coefficient of determination will be:

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Question 38

Which of the following best describes the range of the coefficient of determination?

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Question 39

A statistician estimated the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \varepsilon$ , with 45 observations. The computer output is shown below. However, because of a printer malfunction, some of the results are not shown. These are indicated by the boldface letters a to l. Fill in the missing results (up to three decimal places). Predictor Coef StDev t Constant 2.794 a 6.404 b 0.007 -0.025 0.383 0.072 c se = d R2 = e. ANALYSIS OF VARIANCE Source of Variation df SS MS F Regression f i j l Error g 11.884 k Total h 26.887

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Question 40

In regression analysis, the total variation in the dependent variable y, measured by $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }$ , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Multicollinearity is a situation in which the independent variables are highly correlated with the dependent variable.

Test the hypotheses: $H _ { 0 } :$ There is no first-order autocorrelation HA : There is first-order autocorrelation, given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and $\alpha =$ 0.05.

For a multiple regression model:

For the estimated multiple regression model ŷ = 30  4x1 + 5x2 +3 x3, a one unit increase in x3, holding x1 and x2 constant, will result in which of the following changes in y?

In multiple regression, because of a commonly occurring problem called multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

Which of the following is used to test the significance of the overall regression equation?

A multiple regression analysis that includes 4 independent variables results in a sum of squares for regression of 1200 and a sum of squares for error of 800. The coefficient of determination will be:

Which of the following best describes the range of the coefficient of determination?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 16: Multiple Regression

In regression analysis, the total variation in the dependent variable y, measured by ∑(yi−yˉ)2\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }∑(yi​−yˉ​)2 , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Multicollinearity is a situation in which the independent variables are highly correlated with the dependent variable.

Test the hypotheses: H0:H _ { 0 } :H0​: There is no first-order autocorrelation HA : There is first-order autocorrelation, given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and α=\alpha =α= 0.05.

For a multiple regression model:

For the estimated multiple regression model ŷ = 30  4x1 + 5x2 +3 x3, a one unit increase in x3, holding x1 and x2 constant, will result in which of the following changes in y?

In multiple regression, because of a commonly occurring problem called multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

Which of the following is used to test the significance of the overall regression equation?

A multiple regression analysis that includes 4 independent variables results in a sum of squares for regression of 1200 and a sum of squares for error of 800. The coefficient of determination will be:

Which of the following best describes the range of the coefficient of determination?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Time-Series Analysis and Forecasting

Index Numbers

Filters

In regression analysis, the total variation in the dependent variable y, measured by $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }$ , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Test the hypotheses: $H _ { 0 } :$ There is no first-order autocorrelation HA : There is first-order autocorrelation, given that the Durbin-Watson statistic d = 1.89, n = 28, k = 3 and $\alpha =$ 0.05.