Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

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. $\sum X$ = 30 $\sum X ^ { 2 }$ = 104 $\sum Y$ = 40 $\sum Y ^ { 2 }$ = 178 $\sum X Y$ = 134 -Calculate the coefficient of determination.

Provide an interpretation of the slope estimate.

Test to determine if there is a significant correlation between x and y Use H₀: ? = 0 versus H_a: ? ? 0 by setting $\alpha$ = .01 Reject the null hypothesis,there is a significant correlation between x and y

The _____ of the simple linear regression model is the mean value of y when x = 0.

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 \_\_\_ -Calculate the t statistic and then using appropriate rejection point,test H₀:

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 -Calculate the t statistic and then using appropriate rejection point,test H₀: $\beta _ { 1 }$ = 0 versus Ha: $\beta _ { 1 }$ ? 0 by setting $\alpha$ = .001.What do you conclude about the relationship between y and x?

Any value of the error term in a regression model must be _____ of any other value of the error term.

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 coefficient of determination?

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?

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 -What is the value of regression sum of squares,or the explained variation?

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

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 equation of the least squares line is $\hat { y }$ = 3 + 1x. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196 MSE = 4 -Using the sums of the squares given above,determine the 90% confidence interval for the mean value of monthly tire sales when the advertising expenditure is $5000.

A data set with 7 observed pairs of data (x, y) yielded the following statistics. $\sum X$ =21.57 $\sum X ^ { 2 }$ =68.31 $\sum Y$ =188.9 $\sum Y ^ { 2 }$ =5140.23 $\sum X Y$ =590.83 SSE = unexplained variation = 1.06 -What is the value of SSxx?

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 -What is the degrees of freedom value associated with the error sum of squares,or unexplained variation?

Determine the 95% confidence interval for the average strength of a metal sheet when the average heating time is 2.5 minutes.

Which one of the following statements about the sample correlation coefficient is true?

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

What is the correlation coefficient?

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 estimated slope?

The least squares simple linear regression line minimizes the sum of the vertical deviations between the line and the data points.