Exam 12: Simple Linear Regression

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. Cups of Coffee Sold Temperature 350 50 200 60 210 70 100 80 60 90 40 100 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.

Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided =4 \Sigma=90 \Sigma=340 \Sigma- -)=-156 \Sigma-=234 \Sigma-=1974 =104 -Refer to Exhibit 12-8. The total sum of squares SST) is

Exhibit 12-5 The following information regarding a dependent variable Y) and an independent variable X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 -Refer to Exhibit 12-5. The coefficient of determination is

Regression analysis was applied between sales in $10,000) and advertising in $100) and the following regression function was obtained. = 50 + 8 X $\hat { Y }$ Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales in dollars) is

In a simple regression analysis where Y is a dependent and X an independent variable), if the Y intercept is positive, then

The owner of a bakery wants to analyze the relationship between the expenditure of a customer and the customer's income. A sample of 5 customers is taken and the following information was obtained. Y X Expenditure Income In Thousands 45 20 10.75 19 5.40 22 7.80 25 5.60 14 The least squares estimated line is $\hat { \mathrm { Y } }$ = 4.348 + 0.0826 X. a. Obtain a measure of how well the estimated regression line fits the data. b. You want to test to see if there is a significant relationship between expenditure and income at the 5% level of significance. Be sure to state the null and alternative hypotheses. c. Construct a 95% confidence interval estimate for the average expenditure for all customers with an income of $20,000. d. Construct a 95% confidence interval estimate for the expenditure of one customer whose income is $20,000.

In regression analysis, the variable that is being predicted is the

Exhibit 12-7 You are given the following information about y and x. Dependent Varinble Y) Independent Varinble X) 5 4 7 6 9 2 11 4 -Refer to Exhibit 12-7. The least squares estimate of b? slope) equals

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 point estimate of Y when X = 3 is

Given below are four observations collected in a regression study on two variables x independent variable) and y dependent variable). x y 2 4 0 7 9 8 9 9 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.

The coefficient of correlation

The value of the coefficient of correlation R)

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 point estimate of y when x = 10 is

In regression analysis, if the independent variable is measured in pounds, the dependent variable

In a regression and correlation analysis if R² = 1, then

In the following estimated regression equation $\widehat { y }$ = b? + b?x

If the coefficient of determination is equal to 1, then the coefficient of correlation

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 sample correlation coefficient equals

The interval estimate of the mean value of y for a given value of x is

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. Perform an F test and determine if the price and the number of flash drives sold are related. Let ? = 0.01. b. Perform a t test and determine if the price and the number of flash drives sold are related. Let ? = 0.01.