Question

1. You have a number of variables -- a response variable and some proposed predictors. A correlation matrix may help to give an idea of the strength of the linear relationships present. For the purposes of regression analysis, what would be desirable in terms of … a) …the observed correlation between each proposed predictor and the response variable? (2) b) …the observed correlations among the predictors themselves?

(2) 2. Explain the fact that, over the course of a year, the value of r for the DOW adjusted closing value and the S&P500 adjusted closing value is about 0.98 or higher.

(3) 3. Reconcile these observations: In a regression output, the p-value of the F-test is 2.36 E-06, while the value of R2 is 0.21. (3)

4. What causes the problem of multicollinearity? (2)

5. Interpretation of a regression coefficient: Suppose that in a SLR model, annual salary (in thousands of dollars) is estimated as a function of years of education. With explicit reference to the variable units, interpret the value b1 = 3.42. (3)//15

Answer 1

1. You have a number of variables -- a response variable and some proposed predictors. A correlation matrix may help to give an idea of the strength of the linear relationships present. For the purposes of regression analysis, what would be desirable in terms of …

a) …the observed correlation between each proposed predictor and the response variable?

It is desirable that correlation between each proposed predictor and the response variable is high.

(2) b) …the observed correlations among the predictors themselves?

It is desirable that correlation between observed correlations among the predictors themselves is low.

(2) 2. Explain the fact that, over the course of a year, the value of r for the DOW adjusted closing value and the S&P500 adjusted closing value is about 0.98 or higher.

The high value of correlation of 0.98 shows that there is a positive relation between DOW adjusted closing value and the S&P500 adjusted closing value. When DOW adjusted closing value increases then S&P500 adjusted closing value also increases.

(3) 3. Reconcile these observations: In a regression output, the p-value of the F-test is 2.36 E-06, while the value of R2 is 0.21. (3)

The small p vale ( <0.001) shows that the regression model is significant. But the R square value is 0.21 shows that only 21% of variation in response variable is explained by the predictors. So we have to revise the model.

4. What causes the problem of multicollinearity? (2)

High correlations among the predictor variables causes the problem of multicollinearity.

5. Interpretation of a regression coefficient: Suppose that in a SLR model, annual salary (in thousands of dollars) is estimated as a function of years of education. With explicit reference to the variable units, interpret the value b1 = 3.42. (3)//15

When years of education increases by 1 year, the annual salary in creases by 3.42 (in thousands of dollars) or annual salary in creases by $3420.