Exam 12: Simple Linear Regression

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Refer to Exhibit 12-10. The Y intercept is

A least squares regression line

The coefficient of determination

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

If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable

A regression analysis between demand Y in 1000 units) and price X in dollars) resulted in the following equation = 9 - 3X $\hat { Y }$ The above equation implies that if the price is increased by $1, the demand is expected to

Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable y) and an independent variable x). \Sigma=90 \Sigma- )X -)=466 \Sigma=170 \Sigma-=1434 =10 =505.98 \Sigma-=234 -Refer to Exhibit 12-9. The least squares estimate of b? equals

If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the variation in the independent variable

Given below are five observations collected in a regression study on two variables x independent variable) and y dependent variable). x y 10 7 20 5 30 4 40 2 50 1 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 α = 0.05. d. Compute the coefficient of determination. e. Compute the coefficient of correlation.

It is possible for the coefficient of determination to be

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -Assume you have noted the following prices for books and the number of pages that each book contains. Book Pages x ) Price y) 500 \ 7.00 700 7.50 750 9.00 590 6.50 540 7.50 650 7.00 480 450 a. Perform an F test and determine if the price and the number of pages of the books are related. Let ? = 0.01. b. Perform a t test and determine if the price and the number of pages of the books are related. Let ? = 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.

Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. =4 \Sigma=16 \Sigma=28 \Sigma- -)=-8 \Sigma-=8 =42 =34 -The following data represent the number of flash drives sold per day at a local computer shop and their prices. Price x) Units Sold y) \ 34 3 36 4 32 6 35 5 30 9 38 2 40 1 a. Develop a least-squares regression line and explain what the slope of the line indicates. b. Compute the coefficient of determination and comment on the strength of relationship between x and y. c. Compute the sample correlation coefficient between the price and the number of flash drives sold. Use ?= 0.01 to test the relationship between x and y.

Exhibit 12-2 You are given the following information about y and x. Dependent Variable Y) Independent Variable ) 5 1 4 2 3 3 2 4 1 5 -Refer to Exhibit 12-2. The least squares estimate of b? intercept)equals

If the coefficient of determination is 0.81, the coefficient of correlation