Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

The following results were obtained from a simple regression analysis: $\hat { y }$ = 37.2895 - 1.2024x, r2 = 0.6744, $s _ { b _ { 1 } }$ = 0.2934 -For each unit change in x,the estimated change in the mean of y is equal to:

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 standard error of the model.

The dependent variable is the variable that is being described,predicted,or controlled.

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 -In testing the population slope for significance at a significance level of .05,what is the rejection point condition for the two-sided t test?

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 -Write the equation of the least squares line.

In a simple linear regression analysis,when the constant variance assumption for the error term holds,a plot of the residual versus x:

What is the coefficient of determination?

When using simple regression analysis,if there is a strong positive correlation between the independent and dependent variable,then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.

The following results were obtained as a part of simple linear regression analysis: R²= 0.9162 F test statistic = 81.87 At $\alpha$ = 0)05,the null hypothesis of no linear relationship between the dependent variable and the independent variable _____.

Calculate the correlation coefficient.

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

The point estimate of the error variance in a regression model is:

_____ is a statistical technique in which we use observed data to relate a dependent variable to one or more predictor (independent)variables.

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

If there is significant autocorrelation present in a data set,the error terms are not ________________.

The simple linear regression model assumes there is a _____ relationship between the dependent variable and the independent variable.

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 -Use the least squares regression equation,

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 SSE?

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 -Find the estimated y-intercept.

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 SSE.