# Regression analysis problems

Need help with 4 stats question. This is for an intro stats course at a university level. These need to be answered on Excel and I am having trouble using the program. The file with the questions has been attached.

Thanks in advance.

Question 1.

A medical statistician wanted to examine the relationship between the amount of sunshine (x) in hours, and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight counties around the country. These data are shown below.

Average Daily Sunshine 5 7 6 7 8 6 4 3

Skin Cancer per 100,000 7 11 9 12 15 10 7 5

a. Determine the least squares regression line.

b. Draw a scatter diagram of the data and plot the least squares regression line on it.

c. Estimate the number of skin cancer per 100,000 of population for 6 hours of sunshine.

d. What does the value of the slope of the regression line tell you?

e. Calculate the residual corresponding to the pair (x, y) = (8, 15).

Question 2.

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight counties around the country. These data are shown below.

Average Daily Sunshine 5 7 6 7 8 6 4 3

Skin Cancer per 100,000 7 11 9 12 15 10 7 5

a. Can we conclude at the 1% significance level that there is a linear relationship between sunshine and skin cancer?

b. Calculate the coefficient of determination and interpret it.

c. What does the coefficient of correlation calculated tell you about the direction and strength of the relationship between the two variables?

Question 3.

Narrative: Kylie Minogue Concert

At a recent Kylie Minogue concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year. The following data were collected:

Age 62 57 40 49 67 54 43 65 54 41

Number of Concerts 6 5 4 3 5 5 2 6 3 1

Age 44 48 55 60 59 63 69 40 38 52

Number of Concerts 3 2 4 5 4 5 4 2 1 3

a. Create an Excel output file consists of Descriptive statistics and the least squares regression output. Highlight the key results in your EXCEL output.

b. Use the regression equation to determine the predicted values of y for each values of x..

c. Use the predicted values and the actual values of y to calculate the residuals.

d. Plot the residuals in against the predicted values ?y.

Question 4.

Attempting to analyze the relationship between advertising and sales, the owner of a furniture store recorded the monthly advertising budget ($ thousands) and the sales ($ millions) for a sample of 12 months. The data are listed below.

Advertising 23 46 60 54 28 33

Sales 9.6 11.3 12.8 9.8 8.9 12.5

Advertising 25 31 36 88 90 99

Sales 12.0 11.4 12.6 13.7 14.4 15.9

a. Calculate the least squares line and interpret the coefficients.

b. Determine the standard error of the estimate.

c. Estimate 1β with 95% confidence.

d. Compute the coefficient of determination R2 and interpret this value.

#### Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.