STAT 440 - Forecasting
Lecture Review #4 - Correlation and Regression Inference

A copy of the class handout on formulas for standard errors useful in regression inference is available here.

Review questions:

1) What is the coefficient of determination in regression? How is it interpreted? Why is is popularly called "r-squared"?

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

3) What is a confidence interval? How is it computed? How is it interpreted?

4) What are the basic steps of a statistical hypothesis test? When do we "reject" the null hypothesis? Why?

5) How do we test whether a population correlation is equal to zero? A population slope? What is the relationship between these two tests?

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. Do the appropriate calculations by hand on each of these, to reinforce your understanding of basic principles.

a) Find the sample correlation coefficient for these data.

b) Test H₀: ρ = 0. That is, test to see whether there is a relationship between number of customers and sales volume.

c) Find the slope and intercept of the regression line.

d) Find the error variance for the regression model.

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

2) Repeat Problem #1 using statistical software (Excel, SPSS, R, whatever). On the printout, locate the following quantities: (a) slope, (b) intercept, (c) correlation, (d) r-square, (e) error variance, (f) t-statistic for testing whether the slope (or correlation) is zero, and (g) the p-value for that test.