1 We run a linear regression and the slope estimate is 05 wi

1- We run a linear regression and the slope estimate is 0.5 with standard error of 0.2. What is the largest value of b for which we would NOT reject the null hypothesis that ?1=b? (Assume we are using the 5% significance level)

2- Which of the following indicates a fairly strong relationship between X and Y?

a.R2=0.9

b.The p-value for the null hypothesis ?1=0 is 0.0001

c.The t-statistic for the null hypothesis ?1=0 is 30

3- Suppose we are interested in learning about a relationship between X1 and Y, which we would ideally like to interpret as causal.

True or False? The estimate ?^1 in a linear regression that controls for many variables (that is, a regression with many predictors in addition to X1) is usually a more reliable measure of a causal relationship than ?^1 from a univariate regression on X1.

a.True

b.False

4- According to the balance vs ethnicity model, what is the predicted balance for an Asian in the data set?

5- What is the predicted balance for an African American?

6- According to the model for sales vs TV interacted with radio, what is the effect of an additional unit of radio advertising if TV=50 units?

7- What if TV=250 units?

8- What is the difference between lm(y ~ x*z) and lm(y ~ I(x*z)), when x and z are both numeric variables?

a.The first one includes an interaction term between x and z, whereas the second uses the product of x and z as a predictor in the model.

b.The second one includes an interaction term between x and z, whereas the first uses the product of x and z as a predictor in the model.

c.The first includes only an interaction term for x and z, while the second includes both interaction effects and main effects.

d.The second includes only an interaction term for x and z, while the first includes both interaction effects and main effects.

9- Which of the following statements are true?

a.In the balance vs. income * student model plotted on slide 44, the estimate of beta3 is negative.

b.One advantage of using linear models is that the true regression function is often linear.

c.If the F statistic is significant, all of the predictors have statistically significant effects.

d.In a linear regression with several variables, a variable has a positive regression coefficient if and only if its correlation with the response is positive.

Solution

1)

We run a linear regression and the slope estimate is 0.5 with estimated standard error of 0.2. What is the largest value of b for which we would NOT reject the null hypothesis that 1=b? (assume normal approximation to t distribution, and that we are using the 5% significance level for a two-sided test; need two significant digits of accuracy)

Z value for 5% level of significance for a two sided test =1.96

For not significance, test value z =b/0.2 <1.96

That is b < 1.96*0.2 =0.392

The largest value of b for which we would NOT reject the null hypothesis = 0.392

2) Option B is correct because the p-value=0.0001 for the null hypothesis is extremely small and we can surely reject the null hypothesis of no correlation. Options A and C depends on sample size which is unknown here.

3) False, correlation does not indicate causation.