Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable x) and a dependent variable y). \[\begin{array} { c c } &\text { Caofficient } & \text { Standard Error } \\ \text { Intercept }&- 9.462 & 7.032 \\ x&0.769 & 0.184 \end{array}\] Analysis of Variance SOURCE SS Regression 400 Error Residual) 138 a. Develop the estimated regression line. b. At α = 0.05, test for the significance of the slope. c. At α = 0.05, perform an F test. d. Determine the coefficient of determination.

a. @#IMG-DLM& = -9.462 + 0.769x b. t = 4

Exhibit 12-6 For the following data the value of SSE = 0.4130. \[\begin{array} { c c } \text { Dependent Varinble } Y )& \text { Independent Varinble X)} \\ 15 & 4 \\ 17 & 6 \\ 23 & 2 \\ 17 & 4 \end{array}\] -Refer to Exhibit 12-6. The coefficient of determination R²) equals

A) 0.7071 B) -0.7071 C) 0.5 D) -0.5 A) 0.7071 B) -0.7071 C) 0.5 D) -0.5

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable x) and a dependent variable y). \[\begin{array}{l} \begin{array} { l c c } & \text { Coefficient } & \text { Standard Error } \\ \text { Intercept } & 13.251 & 10.77 \\ \mathrm { X } & 0.803 & 0.385 \end{array}\\\\ \text { Analysis of Variance }\\ \begin{array} { l c } \text { SOURCE } & \text { SS } \\ \text { Regression } & \\ \text { Error Residual) } & 41.674 \\ \text { Total } & 71.875 \end{array} \end{array}\] a. Develop the estimated regression line. b. At α = 0.05, test for the significance of the slope. c. At α = 0.05, perform an F test. d. Determine the coefficient of determination.

a. @#IMG-DLM& = 13.251 + 0.803x b. t = 2

Exhibit 12-1 The following information regarding a dependent variable Y) and an independent variable X) is provided. $\begin{array} { l l } Y&X\\4&2\\3&1\\4&4\\6&3\\8&5 \end{array}$ SSE = 6 SST = 16 -Refer to Exhibit 12-1. The coefficient of correlation is

A) 0.7906 B) - 0.7906 C) 0.625 D) 0.375 A) 0.7906 B) - 0.7906 C) 0.625 D) 0.375

Exhibit 12-3 You are given the following information about y and x. $\begin{array}{cc} \text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\ 12 & 4 \\ 3 & 6 \\ 7 & 2 \\ 6 & 4 \end{array}$ -Refer to Exhibit 12-3. The sample correlation coefficient equals

A) -0.4364 B) 0.4364 C) -0.1905 D) 0.1905 A) -0.4364 B) 0.4364 C) -0.1905 D) 0.1905

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. \[\begin{array} { l } \mathrm { n } = 4 \\ \Sigma \mathrm { X } = 16 \\ \Sigma \mathrm { Y } = 28 \\ \Sigma \mathrm { Y } - { \bar { Y )} } \mathrm { X } - \bar { X } ) = - 8 \\ \Sigma \mathrm { X } - \bar { X } ) ^ { 2 } = 8 \\ \mathrm { SST } = 42 \\ \mathrm { SSE } = 34 \end{array}\] -Refer to Exhibit 12-10. The slope of the regression function is

A) -1 B) 1.0 C) 11 D) 0.0 A) -1 B) 1.0 C) 11 D) 0.0

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. \[\begin{array} { l } \mathrm { n } = 4 \\ \Sigma \mathrm { X } = 16 \\ \Sigma \mathrm { Y } = 28 \\ \Sigma \mathrm { Y } - { \bar { Y )} } \mathrm { X } - \bar { X } ) = - 8 \\ \Sigma \mathrm { X } - \bar { X } ) ^ { 2 } = 8 \\ \mathrm { SST } = 42 \\ \mathrm { SSE } = 34 \end{array}\] -Refer to Exhibit 12-10. The point estimate of Y when X = -3 is

A) 11 B) 14 C) 8 D) 0 A) 11 B) 14 C) 8 D) 0

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided \[\begin{array} { l } \mathrm { n } = 4 \\ \Sigma \mathrm { X } = 90 \\ \Sigma \mathrm { Y } = 340 \\ \Sigma \mathrm { Y } - { \bar { Y) } \mathrm { X } } - \bar { X } ) = - 156 \\ \Sigma \mathrm { X } - \bar { X } ) ^ { 2 } = 234 \\ \Sigma \mathrm { Y } - \bar { Y } ) ^ { 2 } = 1974 \\ \mathrm { SSR } = 104 \end{array}\] -Refer to Exhibit 12-8. The sum of squares due to error SSE) is

A) -156 B) 234 C) 1870 D) 1974 A) -156 B) 234 C) 1870 D) 1974

Exhibit 12-5 The following information regarding a dependent variable Y) and an independent variable X) is provided. $\begin{array} { l l } Y&X\\ 1&1\\2&2\\3&3&\\4&4\\5&5 \end{array}$ -Refer to Exhibit 12-5. The least squares estimate of the Y intercept is

A) 1 B) 0 C) -1 D) 3 A) 1 B) 0 C) -1 D) 3

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. \[\begin{array} { l } \mathrm { n } = 4 \\ \Sigma \mathrm { X } = 16 \\ \Sigma \mathrm { Y } = 28 \\ \Sigma \mathrm { Y } - { \bar { Y )} } \mathrm { X } - \bar { X } ) = - 8 \\ \Sigma \mathrm { X } - \bar { X } ) ^ { 2 } = 8 \\ \mathrm { SST } = 42 \\ \mathrm { SSE } = 34 \end{array}\] -Refer to Exhibit 12-10. The coefficient of determination is

A) 0.1905 B) -0.1905 C) 0.4364 D) -0.4364 A) 0.1905 B) -0.1905 C) 0.4364 D) -0.4364

Exhibit 12-3 You are given the following information about y and x. $\begin{array}{cc} \text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\ 12 & 4 \\ 3 & 6 \\ 7 & 2 \\ 6 & 4 \end{array}$ -Refer to Exhibit 12-3. The least squares estimate of b? equals

A) 1 B) -1 C) -11 D) 11 A) 1 B) -1 C) -11 D) 11

Exam 12: Simple Linear Regression

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable x) and a dependent variable y). Caofficient Standard Error Intercept -9.462 7.032 x 0.769 0.184 Analysis of Variance SOURCE SS Regression 400 Error Residual) 138 a. Develop the estimated regression line. b. At α = 0.05, test for the significance of the slope. c. At α = 0.05, perform an F test. d. Determine the coefficient of determination.

(Essay)

4.8/5

(30)

Question 21

If the coefficient of correlation is a positive value, then the regression equation

(Multiple Choice)

5.0/5

(39)

Question 22

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is

(Multiple Choice)

5.0/5

(39)

Question 23

In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is

(Multiple Choice)

4.8/5

(36)

Question 24

Exhibit 12-6 For the following data the value of SSE = 0.4130. Dependent Varinble Y) Independent Varinble X) 15 4 17 6 23 2 17 4 -Refer to Exhibit 12-6. The coefficient of determination R²) equals

(Multiple Choice)

4.9/5

(30)

Question 25

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable x) and a dependent variable y). Coefficient Standard Error Intercept 13.251 10.77 0.803 0.385 Analysis of Variance SOURCE SS Regression Error Residual) 41.674 Total 71.875 a. Develop the estimated regression line. b. At α = 0.05, test for the significance of the slope. c. At α = 0.05, perform an F test. d. Determine the coefficient of determination.

(Essay)

4.9/5

(35)

Question 26

The following data show the results of an aptitude test Y) and the grade point average of 10 students. Aptitude Test Score Y) GPA X) 26 1.8 31 2.3 28 2.6 30 2.4 34 2.8 38 3.0 41 3.4 44 3.2 40 3.6 43 3.8 a. Develop a least squares estimated regression line. b. Compute the coefficient of determination and comment on the strength of the regression relationship. c. Is the slope significant? Use a t test and let α = 0.05. d. At 95% confidence, test to determine if the model is significant i.e., perform an F test).

(Essay)

4.8/5

(39)

Question 27

Exhibit 12-1 The following information regarding a dependent variable Y) and an independent variable X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 -Refer to Exhibit 12-1. The coefficient of correlation is

(Multiple Choice)

4.8/5

(33)

Question 28

Exhibit 12-3 You are given the following information about y and x. Dependent Variable Y) Independent Variable ) 12 4 3 6 7 2 6 4 -Refer to Exhibit 12-3. The sample correlation coefficient equals

(Multiple Choice)

4.8/5

(41)

Question 29

In regression analysis if the dependent variable is measured in dollars, the independent variable

(Multiple Choice)

4.8/5

(39)

Question 30

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The slope of the regression function is

(Multiple Choice)

4.9/5

(35)

Question 31

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The point estimate of Y when X = -3 is

(Multiple Choice)

4.8/5

(39)

Question 32

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided =4 \Sigma=90 \Sigma=340 \Sigma- -)=-156 \Sigma-=234 \Sigma-=1974 =104 -Refer to Exhibit 12-8. The sum of squares due to error SSE) is

(Multiple Choice)

4.7/5

(33)

Question 33

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x $\hat { Y }$ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales in dollars) is

(Multiple Choice)

4.7/5

(35)

Question 34

Shown below is a portion of a computer output for a regression analysis relating Y demand) and X unit price). ANOVA df SS Regression 1 5048.818 Residual 46 3132.661 Total 47 8181.479 Coefficients Standard Error Intercept 80.390 3.102 -2137 0248 a. Perform a t test and determine whether or not demand and unit price are related. Let α = 0.05. b. Perform an F test and determine whether or not demand and unit price are related. Let α = 0.05. c. Compute the coefficient of determination and fully interpret its meaning. Be very specific. d. Compute the coefficient of correlation and explain the relationship between demand and unit price.

(Essay)

4.9/5

(32)

Question 35

In a regression analysis the standard error is determined to be 4. In this situation the MSE

(Multiple Choice)

4.8/5

(37)

Question 36

Exhibit 12-5 The following information regarding a dependent variable Y) and an independent variable X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 -Refer to Exhibit 12-5. The least squares estimate of the Y intercept is

(Multiple Choice)

4.7/5

(34)

Question 37

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x $\hat { Y }$ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. To perform an F test, the p-value is

(Multiple Choice)

4.8/5

(33)

Question 38

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The coefficient of determination is

(Multiple Choice)

4.8/5

(33)

Question 39

Exhibit 12-3 You are given the following information about y and x. Dependent Variable Y) Independent Variable ) 12 4 3 6 7 2 6 4 -Refer to Exhibit 12-3. The least squares estimate of b? equals

(Multiple Choice)

4.8/5

(31)

Question 40

If the coefficient of correlation is a positive value, then the regression equation

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is

In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is

Exhibit 12-6 For the following data the value of SSE = 0.4130. Dependent Varinble Y) Independent Varinble X) 15 4 17 6 23 2 17 4 -Refer to Exhibit 12-6. The coefficient of determination R²) equals

Exhibit 12-1 The following information regarding a dependent variable Y) and an independent variable X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 -Refer to Exhibit 12-1. The coefficient of correlation is

Exhibit 12-3 You are given the following information about y and x. Dependent Variable Y) Independent Variable ) 12 4 3 6 7 2 6 4 -Refer to Exhibit 12-3. The sample correlation coefficient equals

In regression analysis if the dependent variable is measured in dollars, the independent variable

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The slope of the regression function is

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The point estimate of Y when X = -3 is

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided =4 \Sigma=90 \Sigma=340 \Sigma- -)=-156 \Sigma-=234 \Sigma-=1974 =104 -Refer to Exhibit 12-8. The sum of squares due to error SSE) is

In a regression analysis the standard error is determined to be 4. In this situation the MSE

Exhibit 12-5 The following information regarding a dependent variable Y) and an independent variable X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 -Refer to Exhibit 12-5. The least squares estimate of the Y intercept is

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x $\hat { Y }$ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. To perform an F test, the p-value is

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The coefficient of determination is

Exhibit 12-3 You are given the following information about y and x. Dependent Variable Y) Independent Variable ) 12 4 3 6 7 2 6 4 -Refer to Exhibit 12-3. The least squares estimate of b? equals

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Multiple Regression

Filters

Exam 12: Simple Linear Regression

If the coefficient of correlation is a positive value, then the regression equation

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is

In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is

Exhibit 12-6 For the following data the value of SSE = 0.4130. Dependent Varinble Y) Independent Varinble X) 15 4 17 6 23 2 17 4 -Refer to Exhibit 12-6. The coefficient of determination R²) equals

Exhibit 12-1 The following information regarding a dependent variable Y) and an independent variable X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 -Refer to Exhibit 12-1. The coefficient of correlation is

Exhibit 12-3 You are given the following information about y and x. Dependent Variable Y) Independent Variable ) 12 4 3 6 7 2 6 4 -Refer to Exhibit 12-3. The sample correlation coefficient equals

In regression analysis if the dependent variable is measured in dollars, the independent variable

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The slope of the regression function is

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The point estimate of Y when X = -3 is

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided =4 \Sigma=90 \Sigma=340 \Sigma- -)=-156 \Sigma-=234 \Sigma-=1974 =104 -Refer to Exhibit 12-8. The sum of squares due to error SSE) is

In a regression analysis the standard error is determined to be 4. In this situation the MSE

Exhibit 12-5 The following information regarding a dependent variable Y) and an independent variable X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 -Refer to Exhibit 12-5. The least squares estimate of the Y intercept is

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x Y^\hat { Y }Y^ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. To perform an F test, the p-value is

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The coefficient of determination is

Exhibit 12-3 You are given the following information about y and x. Dependent Variable Y) Independent Variable ) 12 4 3 6 7 2 6 4 -Refer to Exhibit 12-3. The least squares estimate of b? equals

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Multiple Regression

Filters

Exhibit 12-4 Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained. = 12 + 1.8 x $\hat { Y }$ n = 17 SSR = 225 SSE = 75 Sb₁ = 0.2683 -Refer to Exhibit 12-4. To perform an F test, the p-value is