Question

5. Find the 99% prediction interval for the test score of a person who spent 7 hours preparing for the test given that E = 34.677. Interpret the result.

6. Find the explained variation

7. Find the unexplained variation

8. Find the total variation

9. Find the value of r2 and explain its meaning.

10. If the data point (3,100) is added to the data set, how would this effect the results of the regression analysis? Is this data point an outlier, influential point or both? Explain.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. Use this data set to answer the questions below:

x    Hours of preparation      5     2     9      6   10

y    Test score                        64   48   72    73   80

Answer 1

Y'=a+bX

	Coefficients	Standard Error	t Stat	P-value
Intercept	44.84466019	5.900884296	7.599651	0.004728
X	3.524271845	0.841268345	4.189236	0.0248

5) at 99% prediction E= 34.8376 and X=7

Prediction interval:

6)

X	Y	Y'	(Y'-Ybar)^2	(Y-Y')^2
5	64	62.46602	24.34416441	2.353096
2	48	51.8932	240.4607259	15.15704
9	72	76.56311	83.96252614	20.82194
6	73	65.99029	1.987278732	49.13602
10	80	80.08738	160.9695768	0.007635
Mean	67.4	Sum	511.7242719	87.47573

Explined variation:

7) Unexplained variation:

8) Total variaiton:

9)R-squared value:

10)

Ther eis a huge influence by data point(3,100).

It reduced the percentage of variation to 0.0369 or 3.69%

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.192306898
R Square	0.036981943
Adjusted R Square	-0.203772571
Standard Error	18.90715018
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	54.91202186	54.91202186	0.153608514	0.715095594
Residual	4	1429.921311	357.4803279
Total	5	1484.833333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	66.7704918	17.28805933	3.862231759	0.018112799	18.7711441	114.7698
X	1.039344262	2.651867246	0.39192922	0.715095594	-6.323419573	8.402108