Question

• The following output comes from regression using the actual HW9 scores and the test scores from an introductory class taught three years ago.

Sample size: 48
R (correlation coefficient) = 0.4961
R-sq = 0.24614276
Estimate of error standard deviation: 14.458866
Parameter estimates:

Parameter	Estimate	Std. Err.	DF	T-Stat	P-Value
Intercept	47.97618	5.5324807	46	8.671731	<0.0001
Slope	0.3491367	0.090088144	46	3.8755014	0.0003

• Statistical Hypotheses:
• Alpha level:
• Critical value of z:
• Conclusion regarding the null:
• Conclusion in context of the situation:
• Everybody does differently on the test after HW9 , which means there is a lot of variability on the test. How much of that variability is explained by HW9?

Answer 1

Statistical Hypotheses:

H0: β1 = 0, H1: β1 ≠ 0

Alpha level: 0.05

Critical value:

Degrees of freedom: df = n-2 = 48-2 = 46

Critical value (Using T.INV,2T(probability,df)) = T.INV.2T(0.05,46) = 2.013

Conclusion regarding the null: Since p-value = 0.0003, is less than 0.05, we reject the null hypothesis.

Conclusion in context of the situation: β1 ≠ 0. HW9 scores is a significant predictor of test scores

How much of that variability is explained by HW9?

R-sq = 0.24614276

24.61% oof variability is explained by HW9 scores.