Question

1. You work for a consulting company and a client has given your boss the data from below. The client is very interested in establishing a statistically significant relationship between X1 and Y. Your boss knows very little about econometrics and assigns you and your team the project. For this question you should assume that the population regression is appropriately modeled with a simple regression model, i.e. you do not have to consider the possibility of adding more X-regressors to the model. Y is the dependent variable in this model.

Estimate this simple regression and conduct a four-step hypothesis for the significance of the estimated coefficient on X1. Be sure to include both the p-value and critical value approaches. Will your boss be happy when you explain this result? Explain why or why not.

data for problem

Y	X1
600	0
400	0
900	0
600	11
500	0
600	44
800	0
400	11
700	22
700	39
800	0
800	78
600	67
600	0
800	78
600	0
500	17
1100	33
900	0

Answer 1

Copy data in excel.

Click on Data->Data Analysis->Regression.

Enter Y and x values.

Click ok.

The regression output is shown below:

Step 1: H0: Regression model is not significant

             H1: Regression model is significant

Step 2: The test statistic is F=0.73.

Step 3: At alpha = 0.05, the critical value of F = 4.45. Since the critical value of F > 0.73 (the test statistic), fail to reject null hypothesis.

The p-value = 0.4050 > 0.05 (alpha), fail to reject null hypothesis.

Step 4: Since null hypothesis is not rejected, we can conclude that regression model is not significant. The variable x1 is not a good predictor of y.