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.

Age   GPA   Number of Tickets
21   2   4
19   2   7
25   2   5
21   2   1
20   4   8
25   4   4
24   3   1
20   2   3
22   4   3

1.) Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

2.) Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.05 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. y = ___ + ___x1+____x2 or there is not enough evidence

If you can guide me on how to find the p-value in excel that would be much appreciated!

Cheers

Answer 1

The output is generated by using R-software. The r-codes are given below with output.

> Age=c(21,19,25,21,20,25,24,20,22)
> GPA=c(2,2,2,2,4,4,3,2,4)
> Number_of_Tickets=c(4,7,5,1,8,4,1,3,3)
> model=lm(Number_of_Tickets~Age+GPA)
> summary(model)

Call:
lm(formula = Number_of_Tickets ~ Age + GPA)

Residuals:
Min 1Q Median 3Q Max
-2.8683 -1.7806 0.1316 2.2392 2.9165

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.8804 8.5743 1.386 0.215
Age -0.4462 0.4050    -1.102 0.313
GPA 0.6792 0.9422 0.721 0.498

Residual standard error: 2.492 on 6 degrees of freedom
Multiple R-squared: 0.1898,   Adjusted R-squared: -0.08026
F-statistic: 0.7028 on 2 and 6 DF, p-value: 0.5318

conclusion:)

1) p-value= 0.5318

2) Here p-value=0.5318 > alpha= 0.05,

indicate that there is not enough evidence to show that the relationship is statistically significant.

y = 11.8804 -0.4462 * x1+ 0.6792 x2, i.e., y = 11.8804 -0.4462 * Age+ 0.6792 GPA or there is not enough evidence.

(p-value in excel

=F.DIST.RT(test statistic value, n1= numerator degrees of freedom, denominator degrees of freedom)

=F.DIST.RT(0.7028, 2,6)

0.531830204728458

)