Question 1

In simple regression analysis, the quantity Σ(Ŷ − Ȳ)2 is called the ________ sum of squares.

Accepted Answer

A)  total 
B)  explained 
C)  unexplained 
D)  error 
A)  total 
B)  explained 
C)  unexplained 
D)  error B

Question 2

In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the

Accepted Answer

A)  coefficient of determination. 
B)  slope of the regression line. 
C)  y-intercept of the regression line. 
D)  correlation coefficient. 
E)  standard error. 
A)  coefficient of determination. 
B)  slope of the regression line. 
C)  y-intercept of the regression line. 
D)  correlation coefficient. 
E)  standard error. B

Question 3

Consider the following partial computer output from a simple linear regression analysis.
   S = .4862R-Sq = ________
Analysis of Variance
   Test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α = .001. What do you conclude about the relationship between y and x?

Accepted Answer

Since our calculated t - value is −5.908 which is less than the critical value of −4.221 we reject the null hypothesis and conclude there is a significant linear relationship between x and y.
−.34655/.05866 = −5.908, compared to t statistic of −4.221 (for α = .001, df = 13). Thus, reject the null hypothesis at .001. There is a significant linear relationship between x and y.

Question 4

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.
∑X = 24
∑X2 = 124
∑Y = 42
∑Y2 = 338
∑XY = 196
Determine the value of the F statistic.

Accepted Answer

F = 7.00 @#IMG-DLM& SS_XY = 196 − @#IMG-DLM& = 28 SS

Question 5

A data set with 7 observations yielded the following. Use the simple linear regression model.
∑X = 21.57
∑X2 = 68.31
∑Y = 188.9
∑Y2 = 5,140.23
∑XY = 590.83
SSE = 1.117
Calculate the correlation coefficient.

Accepted Answer

r = .987 SS_XY = 590.83

Question 6

An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model.
∑X = 30
∑X2 = 104
∑Y = 40
∑Y2 = 178
∑XY = 134
Determine the value of the F statistic.

Accepted Answer

F = 7 SS_XY = 134 − @#IMG-DLM& =

Question 7

In a simple linear regression model, the intercept term is the mean value of y when x equals ________.

Accepted Answer

A)  1 
B)  0 
C)  −1 
D)  y 
A)  1 
B)  0 
C)  −1 
D)  y

Question 8

Consider the following partial computer output from a simple linear regression analysis.
     Analysis of Variance
   Calculate the MSE.

Accepted Answer

.2364
MSE

Question 9

Consider the following partial computer output from a simple linear regression analysis.
   S = .4862R-Sq = ________
Analysis of Variance
   Test to determine if there is a significant correlation between x and y. Use H0: ρ = 0 versus Ha: ρ ≠ 0 with α = .01. Show the test statistic used in the decision.

Accepted Answer

t = −5.908 < −3.012. Reject H₀; there is

Question 10

A data set with 7 observations yielded the following. Use the simple linear regression model.
∑X = 21.57
∑X2 = 68.31
∑Y = 188.9
∑Y2 = 5,140.23
∑XY = 590.83
SSE = 1.117
Find the estimated slope.

Accepted Answer

b₁ = 4.745

Question 11

If r = −1, then we can conclude that there is a perfect relationship between X and Y.

Accepted Answer

A) True 
 B)False

Question 12

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.
∑X = 24
∑X2 = 124
∑Y = 42
∑Y2 = 338
∑XY = 196
Determine the values of SSE and SST.

Accepted Answer

SSE = 16, SST = 44 SS_XY = 196 −

Question 13

An experiment was performed on a certain metal to determine if the strength is a function of heating time. You use a sample size of 10 to test this hypothesis. The simple linear regression equation is ŷ = 1 + 1X, and the sample coefficient of determination (r2) = .7777. The time is in minutes and the strength is measured in pounds per square inch. Test to determine if there is a significant correlation between the heating time and strength of the metal. Using H0: ρ = 0 vs. HA: ρ ≠ 0 at α = .05, determine the test statistic and decision.

Accepted Answer

Since our calculated t = 5.292 is larger

Question 14

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression equation of the least squares line is ŷ = 3 + 1x.
∑X = 24
∑X2 = 124
∑Y = 42
∑Y2 = 338
∑XY = 196
MSE = 4
Use the least squares regression equation and estimate the monthly tire sales when advertising expenditures = $4,000.

Accepted Answer

7,000 tire

Question 15

The following results were obtained from a simple regression analysis.
Ŷ = 37.2895 − (1.2024)X
r2 = .6744sb = .2934
What is the proportion of the variation explained by the simple linear regression model?

Accepted Answer

.6774
The coefficient of deter

Question 16

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.
∑X = 24
∑X2 = 124
∑Y = 42
∑Y2 = 338
∑XY = 196
Find the rejection point for the t statistic at α = .05 and test H0: β1 ≤ 0 vs. Hα: β1 > 0.

Accepted Answer

t_.05,4 = 2.132; Since our calculated t = 2.64

Question 17

Which of the following is a violation of the independence assumption?

Accepted Answer

A)  negative autocorrelation 
B)  a pattern of cyclical error terms over time 
C)  positive autocorrelation 
D)  a pattern of alternating error terms over time 
E)  All of the other choices are correct. 
A)  negative autocorrelation 
B)  a pattern of cyclical error terms over time 
C)  positive autocorrelation 
D)  a pattern of alternating error terms over time 
E)  All of the other choices are correct.

Question 18

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.
∑X = 24
∑X2 = 124
∑Y = 42
∑Y2 = 338
∑XY = 196
Calculate the sample correlation coefficient.

Accepted Answer

r = .7977. SS_XY = 196

Question 19

In simple regression analysis, the standard error is ________ greater than the standard deviation of y values.

Accepted Answer

A)  always 
B)  sometimes 
C)  never 
A)  always 
B)  sometimes 
C)  never

Question 20

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

Accepted Answer

A) True 
 B)False

In simple regression analysis, the quantity Σ(Ŷ − Ȳ)² is called the ________ sum of squares.

In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the

Consider the following partial computer output from a simple linear regression analysis. S = .4862R-Sq = ________ Analysis of Variance Test H₀: β₁ = 0 versus H_a: β₁ ≠ 0 by setting α = .001. What do you conclude about the relationship between y and x?

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X² = 68.31 ∑Y = 188.9 ∑Y² = 5,140.23 ∑XY = 590.83 SSE = 1.117 Calculate the correlation coefficient.

An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. ∑X = 30 ∑X² = 104 ∑Y = 40 ∑Y² = 178 ∑XY = 134 Determine the value of the F statistic.

In a simple linear regression model, the intercept term is the mean value of y when x equals ________.

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance Calculate the MSE.

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X² = 68.31 ∑Y = 188.9 ∑Y² = 5,140.23 ∑XY = 590.83 SSE = 1.117 Find the estimated slope.

If r = −1, then we can conclude that there is a perfect relationship between X and Y.

The following results were obtained from a simple regression analysis. Ŷ = 37.2895 − (1.2024)X r² = .6744s_b = .2934 What is the proportion of the variation explained by the simple linear regression model?

Which of the following is a violation of the independence assumption?

In simple regression analysis, the standard error is ________ greater than the standard deviation of y values.

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

An Introduction to Business Statistics and Analytics

Descriptive Statistics and Analytics: Tabular and Graphical Methods

Descriptive Statistics and Analytics: Numerical Methods

Probability and Probability Models

Predictive Analytics I: Trees, K-Nearest Neighbors, Naive Bayes,

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Chi-Square Tests

Multiple Regression and Model Building

Predictive Analytics Ii: Logistic Regression, Discriminate Analysis,

Time Series Forecasting and Index Numbers

Nonparametric Methods

Decision Theory

Filters

Exam 14: Simple Linear Regression Analysis

In simple regression analysis, the quantity Σ(Ŷ − Ȳ)2 is called the ________ sum of squares.

In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the

Consider the following partial computer output from a simple linear regression analysis. S = .4862R-Sq = ________ Analysis of Variance Test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α = .001. What do you conclude about the relationship between y and x?

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X2 = 68.31 ∑Y = 188.9 ∑Y2 = 5,140.23 ∑XY = 590.83 SSE = 1.117 Calculate the correlation coefficient.

An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. ∑X = 30 ∑X2 = 104 ∑Y = 40 ∑Y2 = 178 ∑XY = 134 Determine the value of the F statistic.

In a simple linear regression model, the intercept term is the mean value of y when x equals ________.

Consider the following partial computer output from a simple linear regression analysis. Analysis of Variance Calculate the MSE.

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X2 = 68.31 ∑Y = 188.9 ∑Y2 = 5,140.23 ∑XY = 590.83 SSE = 1.117 Find the estimated slope.

If r = −1, then we can conclude that there is a perfect relationship between X and Y.

The following results were obtained from a simple regression analysis. Ŷ = 37.2895 − (1.2024)X r2 = .6744sb = .2934 What is the proportion of the variation explained by the simple linear regression model?

Which of the following is a violation of the independence assumption?

In simple regression analysis, the standard error is ________ greater than the standard deviation of y values.

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

An Introduction to Business Statistics and Analytics

Descriptive Statistics and Analytics: Tabular and Graphical Methods

Descriptive Statistics and Analytics: Numerical Methods

Probability and Probability Models

Predictive Analytics I: Trees, K-Nearest Neighbors, Naive Bayes,

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Chi-Square Tests

Multiple Regression and Model Building

Predictive Analytics Ii: Logistic Regression, Discriminate Analysis,

Time Series Forecasting and Index Numbers

Nonparametric Methods

Decision Theory

Filters

In simple regression analysis, the quantity Σ(Ŷ − Ȳ)² is called the ________ sum of squares.

Consider the following partial computer output from a simple linear regression analysis. S = .4862R-Sq = ________ Analysis of Variance Test H₀: β₁ = 0 versus H_a: β₁ ≠ 0 by setting α = .001. What do you conclude about the relationship between y and x?

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X² = 68.31 ∑Y = 188.9 ∑Y² = 5,140.23 ∑XY = 590.83 SSE = 1.117 Calculate the correlation coefficient.

An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model. ∑X = 30 ∑X² = 104 ∑Y = 40 ∑Y² = 178 ∑XY = 134 Determine the value of the F statistic.

A data set with 7 observations yielded the following. Use the simple linear regression model. ∑X = 21.57 ∑X² = 68.31 ∑Y = 188.9 ∑Y² = 5,140.23 ∑XY = 590.83 SSE = 1.117 Find the estimated slope.

The following results were obtained from a simple regression analysis. Ŷ = 37.2895 − (1.2024)X r² = .6744s_b = .2934 What is the proportion of the variation explained by the simple linear regression model?