Test the hypothesis that the slope is zero

Reference no: EM132176772

ECONOMETRICS ASSIGNMENT -

EXERCISES FOR HYPOTHESIS TESTING & CONFIDENCE INTERVALS

Question 1 - The general manager of an engineering firm wants to know whether a technical artist's experience influences the quality of his or her work. A random sample of 24 artists is selected and their years of work experience and quality rating (as assessed by their supervisors) recorded. Work experience (EXPER) is measured in years and quality rating (RATING) takes a value of 1 through 7, with 7 = excellent and 1 = poor.

The simple regression model RATING = b1 + b2 x EXPER + e is proposed. The least squares estimates of the model and the standard errors of the estimates are:

a. Construct a 95% confidence interval for b₂, the slope of the relationship between quality rating and experience. In what are you 95% confident?

b. Test the null hypothesis that b₂ is zero against the alternative that it is not using the a = 0.05 level of significance. What do you conclude?

c. Test the null hypothesis that b₂ is zero against the one-tail alternative that it is positive at the a = 0.05 level of significance. What do you conclude?

d. For the test in part (b), the p-value is 0.0982. If we choose the probability of a Type I error to be a = 0.05, do we reject the null hypothesis, or not, just based on an inspection of the p-value?

Question 2 - In an estimated simple regression model, based on 24 observations, the estimated slope parameter is 0.310 and the estimated standard error is 0.082.

a. Test the hypothesis that the slope is zero against the alternative that it is not, at the 1% level of significance.

b. Test the hypothesis that the slope is zero against the alternative that it is positive at the 1% level of significance.

c. Test the hypothesis that the slope is zero against the alternative that it is negative at the 5% level of significance.

d. Test the hypothesis that the estimated slope is 0.5, against the alternative that it is not, at the 5% level of significance.

e. Obtain a 99% interval estimate of the slope.

EXERCISES FOR HYPOTHESIS TESTING

Question 1 - The table below presents regression estimates for the relationship between crime and education. Suppose that your sample size N = 42.

	Coefficient	Standard Error
Constant	23.67	7.53
Education	-8.32	2.15

a. Estimate a 95% confidence interval for β2. Show your work carefully. What does this confidence interval tell us about the relationship between x and y.

b. Test at the 99% level the null hypothesis that β2 is zero, versus the alternative hypothesis that it's not. Show your work and write the result clearly. Also write your conclusion.

c. Test at the 95% level the null hypothesis that β1 is zero, versus the alternative that it's positive. Show your work, the result and write your conclusion. Explain in words what does the conclusion mean.

d. Test at the 95% level the null hypothesis that β2 is zero, versus the alternative hypothesis that it is negative. Show your work and write the result clearly. Also write your conclusion. Interpret your result in words using economic theory.

EXERCISES FOR PARAMETER & INTERVAL ESTIMATION

Question 1 - For the regression model y = β₁ + β₂x + e calculate b1, and b₂ and state their interpretation, using the data below.

x_i	y_i
1	8
2	4
3	5
4	3
5	8

Question 2 - You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 97.25 + 33.74 *x

(3.86) (9.42)

What are the endpoints of the interval estimator for β₂ with a 95% interval estimate?

Question 3 - You estimate a simple linear regression model using a sample of 26 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

y = 97.25 + 19.74 *x

(3.86) (3.42)

What are the endpoints of the interval estimator for β₂ with a 98% interval estimate?

Reference no: EM132176772

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