Exam 14: Simple Linear Regression

Exhibit 14-4 Regression analysis was applied between sales data (Y in $1,000s) and advertising data (x in $100s) and the following information was obtained. = 12 + 1.8 x n = 17 SSR = 225 SSE = 75 S_b1 = 0.2683 -Refer to Exhibit 14-4. The critical t value for testing the significance of the slope at 95% confidence is

Given below are four observations collected in a regression study on two variables x (independent variable) and y (dependent variable). a.Develop the least squares estimated regression equation. b.At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. c.Perform an F test to determine whether or not the model is significant. Let $\alpha$ = 0.05. d.Compute the coefficient of determination.

Below you are given a partial computer output based on a sample of 14 observations, relating an independent variable (x) and a dependent variable (y). a.Develop the estimated regression line. b.At $\alpha$ = 0.05, test for the significance of the slope. c.At $\alpha$ = 0.05, perform an F test. d.Determine the coefficient of determination. e.Determine the coefficient of correlation.

Exhibit 14-10 The following information regarding a dependent variable Y and an independent variable X is provided. -Refer to Exhibit 14-10. The coefficient of correlation is

Exhibit 14-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. -Refer to Exhibit 14-5. The coefficient of correlation is

Correlation analysis is used to determine

Exhibit 14-7 You are given the following information about y and x. -Refer to Exhibit 14-7. The coefficient of determination equals

Shown below is a portion of a computer output for a regression analysis relating Y (dependent variable) and X (independent variable). a.Perform a t test using the p-value approach and determine whether or not Y and X are related. Let $\alpha$ = 0.05. b.Using the p-value approach, perform an F test and determine whether or not X and Y are related. c.Compute the coefficient of determination and fully interpret its meaning. Be very specific.

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable (x) and a dependent variable (y). a.Develop the estimated regression line. b.At $\alpha$ = 0.05, test for the significance of the slope. c.At $\alpha$ = 0.05, perform an F test. d.Determine the coefficient of determination.

Exhibit 14-10 The following information regarding a dependent variable Y and an independent variable X is provided. -Refer to Exhibit 14-10. The point estimate of Y when X = -3 is

Given below are five observations collected in a regression study on two variables x (independent variable) and y (dependent variable). a.Develop the least squares estimated regression equation b.At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. c.Perform an F test to determine whether or not the model is significant. Let $\alpha$ = 0.05. d.Compute the coefficient of determination. e.Compute the coefficient of correlation.

Exhibit 14 - 1 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. SSE = 6 SST = 16 -Refer to Exhibit 14-1. The least squares estimate of the slope is

Exhibit 14-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. -Refer to Exhibit 14-5. The least squares estimate of the slope is

Larger values of r² imply that the observations are more closely grouped about the

Shown below is a portion of an Excel output for regression analysis relating Y (dependent variable) and X (independent variable). a. What has been the sample size for the above? b. Perform a t test and determine whether or not X and Y are related. Let $\alpha$ = 0.05. c. Perform an F test and determine whether or not X and Y are related. Let $\alpha$ = 0.05. d. Compute the coefficient of determination. e. Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific.

Jason believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 6 days. Below you are given the results of the sample. a.Which variable is the dependent variable? b.Compute the least squares estimated line. c.Compute the correlation coefficient between temperature and the sales of coffee. d.Is there a significant relationship between the sales of coffee and temperature? Use a .05 level of significance. Be sure to state the null and alternative hypotheses. e.Predict sales of a 90 degree day.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = $\beta$ ₀ + $\beta$ ₁x, is known as

Given below are seven observations collected in a regression study on two variables, X (independent variable) and Y (dependent variable). a.Develop the least squares estimated regression equation. b.At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. c.Perform an F test to determine whether or not the model is significant. Let $\alpha$ = 0.05. d.Compute the coefficient of determination.

Exhibit 14-10 The following information regarding a dependent variable Y and an independent variable X is provided. -Refer to Exhibit 14-10. The MSE is

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 60 - 8X The above equation implies that an