STAT 301 - Business Statistics
Lecture Review #28 - Correlation and Regression Inference

Review questions:

1) What is the error variance (s_e²) for a regression model? How is it calculated?

2) What is the relationship between a t-test for significance of a correlation, and the t-test for the significance of a regression line? When should each be used?

Computational exercises:

1) Anastasia Romanova collects data on the number of customers per day at a small retail store, and the store’s daily sales volume. Data are below:

a) Find the sample correlation coefficient for these data. Test H₀: ρ = 0 — that is, test to see whether there is a relationship between number of customers and sales volume.

b) Compute the slope and intercept of the regression line. Find the error variance (s_e²).

c) Test the null hypothesis that the slope is zero.

2) The "beta coefficient" is a measure of the riskiness of a stock. It is the slope of the regression line between the stock's return (i.e., percentage gain or loss) as the "Y" variable, and the overall market return, the "X" variable. For Sirius Cybernetics Corporation relevant data for four time periods (usually, months) are as follows:

a) What is the "beta coefficient" for Sirius Cybernetics? Give a 95% confidence interval for this quantity.

b) Stocks with beta coefficients of 1 have just as much risk as the overall stock market. Perform an appropriate hypothesis test of H₀: β₁ = 1 vs. H_A: β₁ ≠ 1.

SOLUTIONS:
1) r = 0.992, t = 13.69, slope=20, intercept=0, error variance = 13333.33, t = 13.69
2) slope = 1.2, intercept = 2, error variance = 2.    a) CI: 1.2 +0.45    b) t=1.897