Question 1

Nutritionist A nutritionist is analyzing the cost of an 8 oz.serving of pasta.The nutritionist anticipates that cost is related to: xS1U1B11S1U1B0 = Grams of protein/8 oz. xS1U1B12S1U1B0 = Grams of carbohydrates/8 oz. xS1U1B13S1U1B0 = Grams of fat/8 oz. Using MINITAB,the nutritionist obtained the following results: The regression equation is $$Y = 1.39 + 0.0178 \times 1 - 0.0258 \times 2 - 0.00050 \times 3$$ $\begin{array}{lcll} \text { Predictor } & \text { Coef } & \text { Stdev } &{\text { t-ratio }} \ \text { Constant } & 1.3928 & 0.1096 & 12.71 \ \text { X1 } & 0.017806 & 0.006600 & 2.70 \ \text { X2 } & -0.025825 & 0.001613 & -16.01 \ X 3 & -0.000501 & 0.002779 & -0.18 \end{array}$ $s=0.04805 \quad \mathrm{R}-\mathrm{sq}=97.5 \% \quad \mathrm{R}-\mathrm{sq}(\mathrm{adj})=96.6 \%$ Analysis of Variance $\begin{array}{lllcc} \text { SOURCE } & \text { DF } & & \text { SS } & \text { MS } \ \text { Regression } & & 3 & 0.72562 & 0.24187 \ \text { Error } & 8 & {0.01847} && 0.00231 \ \text { Total } & 11 &&{0.74409} & \end{array}$ -From these regression results,compute a 95% prediction interval for y when x₁ = 4,x₂ = 5,and x₃ = 3.

Accepted Answer

The answer of Nutritionist
A nutritionist is analyzing the cost of...

Question 2

Some computer packages report an adjusted R² along with the unadjusted R².In general,why is the adjusted R² smaller,and under what conditions will it approach the size of the unadjusted R²?

Accepted Answer

The answer of Some computer packages report an adjusted R²...

Question 3

A multiple regression model has three independent variables.The following values of y are given: 
$\begin{array}{llcc}
42&40&40&70&52&28&55&48&60&50
\end{array}$ Compute the total sum of squares (SST).
SST = ____________________

Accepted Answer

The answer of A multiple regression model has three independent...

Question 4

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.If x₁ = 10,x₂ = 4,x₃ = 12,what is the estimated value of y?

Accepted Answer

The answer of Consider the multiple regression equation, \(\hat {...

Question 5

Grade
A statistics teacher collected the following data to determine if the number of hours a student studied during the semester and the number of classes missed could be used to predict the final grade for the course.The following table shows the results of the model being applied to 8 students.
 $$\begin{array} { | c | c | c | } 
\hline \text { Student } & \text { Predicted Grade } & \text { Actural Grade } \
\hline 1 & 84 & 92 \
\hline 2 & 93 & 95 \
\hline 3 & 77 & 81 \
\hline 4 & 81 & 78 \
\hline 5 & 81 & 75 \
\hline 6 & 89 & 88 \
\hline 7 & 88 & 85 \
\hline \mathbf { 8 } & 85 & 85 \
\hline
\end{array}$$
-Calculate the coefficient of multiple determination.

Accepted Answer

The answer of Grade
A statistics teacher collected the following data...

Question 6

In multiple regression and correlation analysis,what is the purpose of the regression component? Of the correlation component?

Accepted Answer

The answer of In multiple regression and correlation analysis,what is...

Question 7

A multiple regression equation has been developed for y = daily attendance at a community swimming pool,x₁ = temperature (degrees Fahrenheit),and x₂ = weekend versus weekday,(x₂ = 1 for Saturday and Sunday,and 0 for other days of the week.)For the regression equation shown below,interpret each partial regression coefficient: $\hat{ Y }$ = 100 + 10x₁ + 175x₂.

Accepted Answer

The answer of A multiple regression equation has been developed...

Question 8

Professor A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \epsilon$$ where: y = final mark (out of 100) xS1U1B11S1U1B0 = number of lectures skipped xS1U1B12S1U1B0 = number of late assignments xS1U1B13S1U1B0 = 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: $$\hat { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$$ $\begin{array}{l|lll|} \hline \text { Predictor } & \text { Coef } & \text { StDev } & T \ \hline \text { Constant } & 41.6 & 17.8 & 2.337 \ x_{1} & -3.18 & 1.66 & -1.916 \ x_{2} & -1.17 & 1.13 & -1.035 \ x_{3} & 0.63 & 0.13 & 4.846 \ \hline \end{array}$ $$S = 13.74$$ $$\mathrm { R } - \mathrm { Sq } = 30.0 \%$$ Analysis of Variance $\begin{array}{l|llll} \hline \text { Source of Variation } & \text { df } & \text { SS } & M S & F \ \hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \ \text { Error } & 46 & 8688 & 188.870 & \ \hline \text { Total } & 49 & 12404 & & \ \hline \end{array}$ -Interpret the coefficients b₁ and b₃. b₁ = ____________________ Interpretation: _____________________________________________________ b₃ = ____________________ Interpretation: _____________________________________________________

Accepted Answer

The answer of Professor
A statistics professor investigated some of the...

Question 9

Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

Accepted Answer

A) True 
 B)False

Question 10

A multiple regression model has three independent variables.The following values of y and $\hat { Y }$ are given: $$\begin{array} { | l | l l l l l l l l l l | } 
\hline y & 40.60 & 39.40 & 38.80 & 70.60 & 49.50 & 25.50 & 52.30 & 46.40 & 56.60 & 47.40 \
\hat { y } & 47.07 & 44.50 & 41.09 & 50.16 & 54.52 & 36.25 & 53.67 & 53.51 & 40.20 & 46.14 \
\hline
\end{array}$$ Compute the multiple standard error of the estimate.

Accepted Answer

The answer of A multiple regression model has three independent...

Question 11

The purpose of the multiple correlation analysis is to measure the strength of the relationship between the dependent (y)and the set of independent (x)variables.

Accepted Answer

A) True 
 B)False

Question 12

Multiple regression analysis examines the linear relationship between a dependent variable (y)and two or more independent variables (x1,x2,and so on).

Accepted Answer

A) True 
 B)False

Question 13

Equation The regression equation, $\hat{ Y }$ = 4 + 1.5xS1U1B11S1U1B0 + 2.5xS1U1B12S1U1B0 has been fitted to 25 data points.The means of xS1U1B11S1U1B0 and xS1U1B12S1U1B0 are 30 and 46,respectively.The sum of the squared differences between observed and predicted values of y has been calculated as SSE = 175,and the sum of the squared differences between y values and mean of y is SST = 525. -What is the approximate 95% prediction interval for an individual y whenever x₁ = 20 and x₂ = 25?

Accepted Answer

The answer of Equation
The regression equation, $\hat{ Y }$ =...

Question 14

Professor
A statistics professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \epsilon$$ where:
y = final mark (out of 100)
xS1U1B11S1U1B0 = number of lectures skipped
xS1U1B12S1U1B0 = number of late assignments
xS1U1B13S1U1B0 = 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:
$$\hat { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$$
$\begin{array}{l|lll|}
\hline \text { Predictor } & \text { Coef } & \text { StDev } & T \
\hline \text { Constant } & 41.6 & 17.8 & 2.337 \
x_{1} & -3.18 & 1.66 & -1.916 \
x_{2} & -1.17 & 1.13 & -1.035 \
x_{3} & 0.63 & 0.13 & 4.846 \
\hline
\end{array}$
$$S = 13.74$$
$$\mathrm { R } - \mathrm { Sq } = 30.0 \%$$
Analysis of Variance
$\begin{array}{l|llll}
\hline \text { Source of Variation } & \text { df } & \text { SS } & M S & F \
\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \
\text { Error } & 46 & 8688 & 188.870 & \
\hline \text { Total } & 49 & 12404 & & \
\hline
\end{array}$
-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?
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________

Accepted Answer

The answer of Professor
A statistics professor investigated some of the...

Question 15

Marketing Analyst A marketing analyst is interested in predicting prospective buyer's knowledge about compact disc players.A random sample of 36 buyers was taken,a questionnaire about compact disc players completed,and information about education,income and age was obtained.In estimating the equation,the variables were: y = knowledge about compact disc players xS1U1B11S1U1B0 = education (years) xS1U1B12S1U1B0 = age xS1U1B13S1U1B0 = income (thousands of dollars) The resulting output using MINITAB was: $$\begin{array}{l} \text { The regression equation is }\ \begin{array} { l c c r } Y = 50.2 + 4.36 \times 1 - 0.632 \times 2 - 0.068 \times 3 & \ & & \ \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } \ \text { Constant } & 50.168 & 4.977 & 10.08 \ X 1 & 4.3609 & 0.4064 & 10.73 \ X 2 & - 0.63169 & 0.08172 & - 7.73 \ X 3 & - 0.0682 & 0.1176 & - 0.58 \ s = 4.615 & \text { R-sq } = 85.0 \% & \text { R-sq(adj) } = 83.6 \% \end{array} \end{array}$$ -Identify b₀,b₁,and b₃. b₀ = ____________________ b₁ = ____________________ b₃ = ____________________

Accepted Answer

The answer of Marketing Analyst
A marketing analyst is interested in...

Question 16

What does the numerical value of the multiple standard error of estimate (s_e)reflect?

Accepted Answer

The answer of What does the numerical value of the...

Question 17

Consider the multiple regression equation, $\hat{ Y }$ = 80 + 15x₁ - 5x₂ + 100x₃.If x₃ were to increase by 5,what change would be necessary in x₂ in order for the estimated value of y to remain unchanged? x₂ would ____________________ by ____________________.

Accepted Answer

The answer of Consider the multiple regression equation, \(\hat{ Y...

Question 18

With four or more variables,the regression equation becomes a mathematical entity called a ____________________.

Accepted Answer

The answer of With four or more variables,the regression equation...

Question 19

Motor Vehicle In order to predict motor vehicle purchases for the U.S.,the coefficients of a multiple regression equation were estimated using 25 years of data.The variables were: y = motor vehicle purchases (billions of dollars) x₁ = disposable personal income (billions of dollars) x₂ = U.S.population (millions of persons) x₃ = automobile installment credit (billions of dollars) Part of the results using MINITAB was: The regression equation is $Y = - 61.3 - 0.0022 \times 1 + 0.368 \times 2 + 0.725 \times 3$ $\begin{array} { l l l l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } \ \text { Constant } & - 61.28 & 36.96 & - 1.66 \ \text { X1 } & - 0.00221 & 0.01504 & - 0.15 \ \text { X2 } & 0.3679 & 0.2001 & 1.84 \ \text { X3 } & 0.7254 & 0.2115 & 3.43 \end{array}$ Analysis of Variance $\begin{array} { l c l } \text { SOURCE } & \text { DF } & \text { SS } \ \text { Regression } & 3 & 32624 \ \text { Error } & 21 & 591 \ \text { Total } & 24 & 33215 \end{array}$ Use the values in the analysis of variance table to find MSR and MSE. MSR = ____________________ MSE = ____________________

Accepted Answer

The answer of Motor Vehicle
In order to predict motor vehicle...

Question 20

Nutritionist A nutritionist is analyzing the cost of an 8 oz.serving of pasta.The nutritionist anticipates that cost is related to: xS1U1B11S1U1B0 = Grams of protein/8 oz. xS1U1B12S1U1B0 = Grams of carbohydrates/8 oz. xS1U1B13S1U1B0 = Grams of fat/8 oz. Using MINITAB,the nutritionist obtained the following results: The regression equation is $$Y = 1.39 + 0.0178 \times 1 - 0.0258 \times 2 - 0.00050 \times 3$$ $\begin{array}{lcll} \text { Predictor } & \text { Coef } & \text { Stdev } &{\text { t-ratio }} \ \text { Constant } & 1.3928 & 0.1096 & 12.71 \ \text { X1 } & 0.017806 & 0.006600 & 2.70 \ \text { X2 } & -0.025825 & 0.001613 & -16.01 \ X 3 & -0.000501 & 0.002779 & -0.18 \end{array}$ $s=0.04805 \quad \mathrm{R}-\mathrm{sq}=97.5 \% \quad \mathrm{R}-\mathrm{sq}(\mathrm{adj})=96.6 \%$ Analysis of Variance $\begin{array}{lllcc} \text { SOURCE } & \text { DF } & & \text { SS } & \text { MS } \ \text { Regression } & & 3 & 0.72562 & 0.24187 \ \text { Error } & 8 & {0.01847} && 0.00231 \ \text { Total } & 11 &&{0.74409} & \end{array}$ -From these regression results,compute a 95% confidence interval for y when x₁ = 4,x₂ = 5,and x₃ = 3.

Accepted Answer

The answer of Nutritionist
A nutritionist is analyzing the cost of...

Exam 16: Multiple Regression and Correlation

Some computer packages report an adjusted R² along with the unadjusted R².In general,why is the adjusted R² smaller,and under what conditions will it approach the size of the unadjusted R²?

A multiple regression model has three independent variables.The following values of y are given: $\begin{array}{llcc}42&40&40&70&52&28&55&48&60&50\end{array}$ Compute the total sum of squares (SST). SST = ____________________

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.If x₁ = 10,x₂ = 4,x₃ = 12,what is the estimated value of y?

In multiple regression and correlation analysis,what is the purpose of the regression component? Of the correlation component?

Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

The purpose of the multiple correlation analysis is to measure the strength of the relationship between the dependent (y)and the set of independent (x)variables.

Multiple regression analysis examines the linear relationship between a dependent variable (y)and two or more independent variables (x₁,x₂,and so on).

What does the numerical value of the multiple standard error of estimate (s_e)reflect?

Consider the multiple regression equation, $\hat{ Y }$ = 80 + 15x₁ - 5x₂ + 100x₃.If x₃ were to increase by 5,what change would be necessary in x₂ in order for the estimated value of y to remain unchanged? x₂ would by .

With four or more variables,the regression equation becomes a mathematical entity called a ____________________.

Exam 16: Multiple Regression and Correlation

Some computer packages report an adjusted R2 along with the unadjusted R2.In general,why is the adjusted R2 smaller,and under what conditions will it approach the size of the unadjusted R2?

A multiple regression model has three independent variables.The following values of y are given: 42404070522855486050\begin{array}{llcc}42&40&40&70&52&28&55&48&60&50\end{array}42​40​40​70​52​28​55​48​60​50​ Compute the total sum of squares (SST). SST = ____________________

Consider the multiple regression equation, Y^\hat { Y }Y^ = 80 + 15x1 - 5 x2 + 100x3.If x1 = 10,x2 = 4,x3 = 12,what is the estimated value of y?

In multiple regression and correlation analysis,what is the purpose of the regression component? Of the correlation component?

Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

The purpose of the multiple correlation analysis is to measure the strength of the relationship between the dependent (y)and the set of independent (x)variables.

Multiple regression analysis examines the linear relationship between a dependent variable (y)and two or more independent variables (x1,x2,and so on).

What does the numerical value of the multiple standard error of estimate (se)reflect?

Consider the multiple regression equation, Y^\hat{ Y }Y^ = 80 + 15x1 - 5x2 + 100x3.If x3 were to increase by 5,what change would be necessary in x2 in order for the estimated value of y to remain unchanged? x2 would ____________________ by ____________________.

With four or more variables,the regression equation becomes a mathematical entity called a ____________________.

Some computer packages report an adjusted R² along with the unadjusted R².In general,why is the adjusted R² smaller,and under what conditions will it approach the size of the unadjusted R²?

A multiple regression model has three independent variables.The following values of y are given: $\begin{array}{llcc}42&40&40&70&52&28&55&48&60&50\end{array}$ Compute the total sum of squares (SST). SST = ____________________

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.If x₁ = 10,x₂ = 4,x₃ = 12,what is the estimated value of y?

Multiple regression analysis examines the linear relationship between a dependent variable (y)and two or more independent variables (x₁,x₂,and so on).

What does the numerical value of the multiple standard error of estimate (s_e)reflect?

Consider the multiple regression equation, $\hat{ Y }$ = 80 + 15x₁ - 5x₂ + 100x₃.If x₃ were to increase by 5,what change would be necessary in x₂ in order for the estimated value of y to remain unchanged? x₂ would by .