Exam 12: Simple Linear Regression

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided -Refer to Exhibit 12-8. The coefficient of correlation is

In simple linear regression analysis, which of the following is not true?

If the coefficient of correlation is a negative value, then the coefficient of determination

The value of the coefficient of correlation (R)

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided -Refer to Exhibit 12-8. The sum of squares due to error (SSE) is

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. -Refer to Exhibit 12-10. The point estimate of Y when X = 3 is

The owner of a retail store randomly selected the following weekly data on profits and advertising cost. a.Write down the appropriate linear relationship between advertising cost and profits. Which is the dependent variable? Which is the independent variable? b.Calculate the least squares estimated regression line. c.Predict the profits for a week when $200 is spent on advertising. d.At 95% confidence, test to determine if the relationship between advertising costs and profits is statistically significant. e.Calculate the coefficient of determination.

If a data set has SSR = 400 and SSE = 100, then the coefficient of determination is

Assume you have noted the following prices for books and the number of pages that each book contains. a.Perform an F test and determine if the price and the number of pages of the books are related. Let $\alpha$ = 0.01. b.Perform a t test and determine if the price and the number of pages of the books are related. Let $\alpha$ = 0.01. c.Develop a 90% confidence interval for estimating the average price of books that contain 800 pages. d.Develop a 90% confidence interval to estimate the price of a specific book that has 800 pages.

In regression analysis, the independent variable is

Exhibit 12-6 For the following data the value of SSE = 0.4130. -Refer to Exhibit 12-6. The coefficient of determination (r²) equals

Exhibit 12-2 You are given the following information about y and x. -Refer to Exhibit 12-2. The sample correlation coefficient equals

SSE can never be

Exhibit 12-1 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. SSE = 6 SST = 16 -Refer to Exhibit 12-1. The least squares estimate of the slope is

If two variables, x and y, have a strong linear relationship, then

Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price). a.Perform a t test and determine whether or not demand and unit price are related. Let $\alpha$ = 0.05. b.Perform an F test and determine whether or not demand and unit price are related. Let $\alpha$ = 0.05. c.Compute the coefficient of determination and fully interpret its meaning. Be very specific. d.Compute the coefficient of correlation and explain the relationship between demand and unit price.

Exhibit 12-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. -Refer to Exhibit 12-5. The MSE is

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). -Refer to Exhibit 12-9. The coefficient of determination equals

The following data shows the yearly income (in $1,000) and age of a sample of seven individuals. a.Develop the least squares regression equation. b.Estimate the yearly income of a 30-year-old individual. c.Compute the coefficient of determination. d.Use a t test to determine whether the slope is significantly different from zero. Let $\alpha$ = 0.05. e.At 95% confidence, perform an F test and determine whether or not the model is significant.

Exhibit 12-7 You are given the following information about y and x. -Refer to Exhibit 12-7. The least squares estimate of b₀ (intercept) equals