Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

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 estimated y-intercept.

Find the rejection point for the t statistic at a = 0.5 and test H₀: b1≤ 0 vs.Ha: b1> 0.

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 -What are the limits of the 99% prediction interval of the daily sales in dollars of an individual grocery store that has spent $3000 on advertising expenditures? The distance value for this particular prediction is reported as .164.

While the range for r² is between 0 and 1,the range for r is between ____ and ____.

In a simple linear regression model,the slope term is the change in the mean value of y associated with a _____ unit increase in x.

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 -Find the estimated slope.

Write the equation of the least squares line.

Determine the 95% confidence interval for the mean value of y when x = 35.Givens: ? x = 277 and ? x² = 8705

In simple regression analysis,the quantity $\sum ( y - \bar { y } ) ^ { 2 }$ Is called the __________ variation.

In simple linear regression,the __________ assumption requires that all variation around the regression line should be equal at all possible values (levels)of the independent variable.

Consider the following partial computer output from a simple linear regression analysis. Predictor Coef SE Coef T P Constant 4.8615 0.5201 9.35 0.000 Independent Var - 0.34655 0.05866 \_\_\_ =0.4862-=\_\_\_\_ Analysis of Variance Source DF SS MS F P Regression 1 \_\_ 34.90 0.000 Residual Error 13 \_\_ \_\_ Total 14 11.3240 -What is the estimated y-intercept?

For the same set of observations on a specified dependent variable y,two different independent variables x₁and x₂were used to fit two separate simple linear regression models.Model 1 used x₁as the independent variable,and Model 2 used x₂as the independent variable.If the r² values from Model 1 and Model 2 were 0.92 and 0.85,respectively,then we can conclude that:

For the same value of x (independent variable),the width of the confidence interval for the average value of y (dependent variable)is ______________ the width of the prediction interval for the individual value of y.

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 coefficient of determination.

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 predicted value of y when x = 35?

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 slope?

The strength of the relationship between two quantitative variables can be measured by:

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 estimated y-intercept?

In performing an F test for a simple linear regression analysis based on 20 observations,the critical F value would have ________ numerator degrees of freedom and _________ denominator degrees of freedom.

What is the predicted value of y when x = 9.00?