Question

The number of days a student is absent in a four week period is recorded along with the test score over the material covered over those four weeks. Consider the output from Excel of a linear regression:
Claim: There is a linear correlation between the number of days missed and the test score over the material covered.

Regression Statistics

Multiple R	.699389593
R squared	.489145802
Adjusted R Square	.446574619
Standard error	14.49517418
error observations	14

Anova

	df	ss	ms	f
Regression	1	2414.179	2414.179	11.49007
residual	12	2521.321	210.1101
total	13	4935.5

	Coefficients	Standard Error	t Stat	P-value
Intercept Classes	82.30589096	5.209439	15.79938	2.14E-09
missed	-3.51664837	1.03751	-3.3897	.005371

What is the correlation coefficient, p value, and degrees of freedom?

Answer 1

• The correlation coefficient is given by 0.6994
• Here we have to test the claim that There is a linear correlation between the number of days missed and the test score over the material covered.
• HYPOTHESIS TO BE TESTED.
• Let the null hypothesis be that there is no linear correlation between the number of days missed and the test score over the material covered.
• Let the alternate hypothesis be that there is a linear correlation between the number of days missed and the test score over the material covered.
• Ho: vs H1:
• TEST STATISTICS
• 
• =3.3897
• PVALUE
• By using r code p value is given by
• Since this is a two sided test
• p.value = 2*pt(t.value, df=length(lengths-2),lower=FALSE)
• 2*pt(3.3897, 12,lower=FALSE)
• =0.005370981
• CONCLUSION
• The p value calculated is less than 5% significant level.
• Hence we do not have enough evidence to reject the null hypothesis.
• Hence we conclude that  there is a linear correlation between the number of days missed and the test score over the material covered.