Consider the following partial computer output from a simple linear regression analysis. \[\begin{array} { l c l c c } \text { Variable } & \text { Coefficient } & \text { Std. Deviation } & \mathrm { T } & \mathrm { P } \\ \text { Intercept } & - 28.13 & & - .088 & .9309 \\ \mathrm { X } & 1.12 & .04891 & 22.895 & .0001 \\ \mathrm { R } ^ { 2 } .9722 & & & & \end{array}\] -What is the estimated y-intercept?

A) -.088 B) 931 C) 22.895 D) -28.13 E) 9722 A) -.088 B) 931 C) 22.895 D) -28.13 E) 9722

A local grocery store wants to predict the daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects the store sales. The manager randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/Mega-Stat output given below summarizes the results of fitting a simple linear regression model using this data. Regression Analysis $\begin{array}{rc} \mathrm{r}^{2} 0.762 & \mathrm{n} 7 \\ \mathrm{R} 0.873 & \mathrm{k} \text { 1 } \\ \text { Std. Error 11.547 } & \text { Dep. Var. Sales } \end{array}$ ANOVA table $\begin{array}{rrrrrr} \hline \text { Source } & S S & d f & M S & F & p \text {-value } \\ \hline \text { Regression } & 2,133.3333 & 1 & 2,133.3333 & 16.00 & .0103 \\ \text { Residual } & 666.6667 & 5 & 133.3333 & & \\ \hline \text { Total } & 2,800.0000 & 6 & & &\\\hline \end{array}$ $\text { Regression output }$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Confidence interval }$ $\begin{array}{rrrrrrrr} \hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \\ & & & & & \text { lower } & \\ \hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \\ \text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & & \end{array}$ -If the manager decides to spend $3000 on advertising,based on the simple linear regression results given above,the estimated average,or predicted,sales is:

A) $68,333 B) $20,063.33 C) $83,334 D) $20,064,333 E) $70,000 A) $68,333 B) $20,063.33 C) $83,334 D) $20,064,333 E) $70,000

Consider the following partial computer output from a simple linear regression analysis: \[\begin{array} { l l c c c } \text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm { T } & \mathrm { P } \\ \text { Constant } & 5566.1 & 254.0 & 21.91 & 0.000 \\ \text { Independent Var } & - 210.35 & 24.19 & - & \end{array}\] S = _________ R-Sq = Analysis of Variance $\begin{array}{lccrcc} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression } & 1 & 3963719 & 3963719 & 75.59 & 0.000 \\ \text { Residual Error } & 14 &\_\_\_ & 52439 & &\\ \text { Total }&15&\_\_\_ \end{array}$ -What is the predicted value of y when x = 8.5?

The answer of Consider the following partial computer output from...

Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

A local tire dealer wants to predict the number of tires sold each month.The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising.The dealer 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. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196 -Calculate the sample correlation coefficient.

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Question 41

In a simple linear regression model,the coefficient of determination indicates the strength and direction of the relationship between independent and dependent variable.

(True/False)

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Question 42

Consider the following partial computer output from a simple linear regression analysis. Variable Coefficient Std. Deviation Intercept -28.13 -.088 .9309 1.12 .04891 22.895 .0001 .9722 -What is the estimated y-intercept?

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Question 43

A local tire dealer wants to predict the number of tires sold each month. The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising. The dealer randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires) and monthly advertising expenditures (in thousands of dollars). Residuals are calculated for all of the randomly selected six months and ordered from smallest to largest. -Determine the normal score for the third residual in the ordered array.

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Question 44

An experiment was performed on a certain metal to determine if the strength is a function of heating time. The sample size consists of ten metal sheets. Residuals are calculated for all ten metal sheets and ordered from smallest to largest. -Determine the normal score for the smallest residual.

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Question 45

A data set with 7 observations yielded the following.Use the simple linear regression model where y is the dependent variable and x is the independent variable. $\sum x$ = 21.57 $\sum X ^ { 2 }$ = 68.31 $\sum Y ^ { 2 }$ = 188.9 $\sum Y ^ { 2 }$ = 5,140.23 $\sum X Y$ = 590.83 SSE = 1.06 -Calculate the correlation coefficient.

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Question 46

An experiment was performed on a certain metal to determine if the strength is a function of heating time. The sample size consists of ten metal sheets. Residuals are calculated for all ten metal sheets and ordered from smallest to largest. -Determine the normal score for the second largest residual (ninth residual in the ordered array).

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Question 47

Consider the following partial computer output from a simple linear regression analysis with a sample size of 16 observations.Use a t test to test the significance of the model at a = .05. Variable Coefficient Std. Deviation Intercept 49.78 19.11 .015104 .006005 =7.0 =31.1\% t = 2.52,reject H₀

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Question 48

A local tire dealer wants to predict the number of tires sold each month.The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising.The dealer 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. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196 -Calculate the standard error.

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Question 49

Determine the 95% prediction interval for the mean value of y when x = 9.00 Given: ∑ x = 129.03 and ∑ x² = 1178.547

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Question 50

A data set with 7 observations yielded the following.Use the simple linear regression model where y is the dependent variable and x is the independent variable. $\sum x$ = 21.57 $\sum X ^ { 2 }$ = 68.31 $\sum Y ^ { 2 }$ = 188.9 $\sum Y ^ { 2 }$ = 5,140.23 $\sum X Y$ = 590.83 SSE = 1.06 -Find the rejection point for the t statistic ( $\alpha$ = .05).Test H₀:b1? 0 vs.Ha:b1> 0. t = 13.993,reject H₀

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Question 51

Use the following results obtained from a simple linear regression analysis with 12 observations: $\hat { y }$ = 37.2895 - 1.2024x,r² = .6744, $s _ { b _ { 1 } }$ = .2934 Test to determine if there is a significant negative linear relationship between the independent and dependent variable at a = .05. Reject H₀.There is a significant negative linear relationship between dependent and independent variable.

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Question 52

Consider the following partial computer output from a simple linear regression analysis. Predictor Coef SE Coef T P Constant 67.05 20.90 3.21 0.012 Independent Var 5.8167 0.7085 \_\_\_ 0.000 S = ___ R-Sq = _ Analysis of Variance Source DF SS MS F P Regression 1 - 34920 67.39 0.000 Residual Error 8 - 518 Total 9 39065 -What is the explained variation?

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Question 53

What is the unexplained variation?

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Question 54

A local grocery store wants to predict the daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects the store sales. The manager randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/Mega-Stat output given below summarizes the results of fitting a simple linear regression model using this data. Regression Analysis 0.762 7 0.873 1 Std. Error 11.547 Dep. Var. Sales ANOVA table Source SS df MS F p -value Regression 2,133.3333 1 2,133.3333 16.00 .0103 Residual 666.6667 5 133.3333 Total 2,800.0000 6 $\text { Regression output }$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Confidence interval }$ Variables Coefficients std. error t(df=5) p-value 95\% 95\% upper lower Intercep 63.3333 7.9682 7.948 .0005 42.8505 83.8162 Advertising 6.6667 1.6667 4.000 .0103 -If the manager decides to spend $3000 on advertising,based on the simple linear regression results given above,the estimated average,or predicted,sales is:

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Question 55

The standard error of the estimate (standard error)is the estimated standard deviation of the distribution of the independent variable x for all values of the dependent variable y.

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Question 56

For a given data set,specific value of x,and a confidence level,if all the other factors are constant,the confidence interval for the mean value of y will _______ be wider than the corresponding prediction interval for the individual value of y.

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Question 57

Consider the following partial computer output from a simple linear regression analysis: Predictor Coef SE Coef Constant 5566.1 254.0 21.91 0.000 Independent Var -210.35 24.19 - S = _________ R-Sq = Analysis of Variance Source DF SS MS F P Regression 1 3963719 3963719 75.59 0.000 Residual Error 14 \_\_\_ 52439 Total 15 \_\_\_ -What is the predicted value of y when x = 8.5?

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Question 58

Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 4 minutes.Provide an interpretation of this interval.

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Question 59

In a simple linear regression analysis,the sample correlation coefficient r and the estimate of the slope b₁_____ have the same sign.

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Question 60

In a simple linear regression model,the coefficient of determination indicates the strength and direction of the relationship between independent and dependent variable.

Consider the following partial computer output from a simple linear regression analysis. Variable Coefficient Std. Deviation Intercept -28.13 -.088 .9309 1.12 .04891 22.895 .0001 .9722 -What is the estimated y-intercept?

An experiment was performed on a certain metal to determine if the strength is a function of heating time. The sample size consists of ten metal sheets. Residuals are calculated for all ten metal sheets and ordered from smallest to largest. -Determine the normal score for the smallest residual.

Consider the following partial computer output from a simple linear regression analysis with a sample size of 16 observations.Use a t test to test the significance of the model at a = .05. Variable Coefficient Std. Deviation Intercept 49.78 19.11 .015104 .006005 =7.0 =31.1\% t = 2.52,reject H₀

Determine the 95% prediction interval for the mean value of y when x = 9.00 Given: ∑ x = 129.03 and ∑ x² = 1178.547

What is the unexplained variation?

The standard error of the estimate (standard error)is the estimated standard deviation of the distribution of the independent variable x for all values of the dependent variable y.

For a given data set,specific value of x,and a confidence level,if all the other factors are constant,the confidence interval for the mean value of y will _______ be wider than the corresponding prediction interval for the individual value of y.

Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 4 minutes.Provide an interpretation of this interval.

In a simple linear regression analysis,the sample correlation coefficient r and the estimate of the slope b₁_____ have the same sign.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

In a simple linear regression model,the coefficient of determination indicates the strength and direction of the relationship between independent and dependent variable.

Consider the following partial computer output from a simple linear regression analysis. Variable Coefficient Std. Deviation Intercept -28.13 -.088 .9309 1.12 .04891 22.895 .0001 .9722 -What is the estimated y-intercept?

An experiment was performed on a certain metal to determine if the strength is a function of heating time. The sample size consists of ten metal sheets. Residuals are calculated for all ten metal sheets and ordered from smallest to largest. -Determine the normal score for the smallest residual.

Consider the following partial computer output from a simple linear regression analysis with a sample size of 16 observations.Use a t test to test the significance of the model at a = .05. Variable Coefficient Std. Deviation Intercept 49.78 19.11 .015104 .006005 =7.0 =31.1\% t = 2.52,reject H0

Determine the 95% prediction interval for the mean value of y when x = 9.00 Given: ∑ x = 129.03 and ∑ x2 = 1178.547

What is the unexplained variation?

The standard error of the estimate (standard error)is the estimated standard deviation of the distribution of the independent variable x for all values of the dependent variable y.

For a given data set,specific value of x,and a confidence level,if all the other factors are constant,the confidence interval for the mean value of y will _______ be wider than the corresponding prediction interval for the individual value of y.

Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 4 minutes.Provide an interpretation of this interval.

In a simple linear regression analysis,the sample correlation coefficient r and the estimate of the slope b1_____ have the same sign.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

Consider the following partial computer output from a simple linear regression analysis with a sample size of 16 observations.Use a t test to test the significance of the model at a = .05. Variable Coefficient Std. Deviation Intercept 49.78 19.11 .015104 .006005 =7.0 =31.1\% t = 2.52,reject H₀

Determine the 95% prediction interval for the mean value of y when x = 9.00 Given: ∑ x = 129.03 and ∑ x² = 1178.547

In a simple linear regression analysis,the sample correlation coefficient r and the estimate of the slope b₁_____ have the same sign.