Question

The following data was collected to explore how a student's age and GPA affect the number of parking tickets they receive in a given year. The dependent variable is the number of parking tickets, the first independent variable (x1x1 ) is the student's age, and the second independent variable (x2x2 ) is the student's GPA.

Effects on Number of Parking Tickets

Age	GPA	Number of Tickets
1717	22	11
1818	22	22
2121	33	33
2121	33	44
2222	33	44
2222	33	55
2323	33	66
2323	33	77
2525	33	77

Step 2 of 2 :

Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.010.01 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.

Answer 1

Carrying out regression between the dependent variable Number of tickets, and the independent variables Age and GPA in Excel (go to Data tab -> Data Analysis -> Regression, choose No. of tickets as the Y-column and Age, GPA as the X-columns), we get the following output:

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-146.7309942	26.09574562	-5.622793704	0.001352247	-210.5849834	-82.87700494
Age	0.107637079	0.023551165	4.570350464	0.003809073	0.050009454	0.165264705
GPA	-1.228070175	1.225979842	-1.001705031	0.355157403	-4.227934779	1.771794429

Hence, as we see above,the p-value of coefficient of Age is 0.0038 which is < 0.01, and hence the linear relationship between No. of tickets and Age is statistically significant at the 0.01 significance level. However, the p-value of GPA is 0.355 >> 0.01, hence the linear relationship between No. of tickets and GPA is not statistically significant at the 0.01 significance level.

Therefore, there isn't enough evidence to show that the relationship between No. of tickets,Age and GPA taken together is statistically significant at the 0.01 significance level.