Question

Number of absences (x) Final exam score (Y)
0                                             89.4
1                                             87.2
2                                            84.5
3                                             81.7
4                                             77.3
5                                             74.8
6                                             63.7
7                                             72.1
8                                             66.4
9                                             65.8

Critical Values for Correlation Coefficient
n
3     0.997
4     0.950
5     0.878
6     0.811
7     0.754
8    0.707
9     0.666
10   0.632
11   0.602
12   0.576
13   0.553
14   0.532
15   0.514
16   0.497
17   0.482
18   0.468
19   0.456
20   0.444
21   0.433
22   0.423
23   0.413
24   0.404
25   0.396
26   0.388
27   0.381
28   0.374
29   0.367
30   0.361
n

A) Find the​ least-squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable.

y with caret = ___x + ___?

B) Interpret the slope and the​ y-intercept.

For every additional​ absence, a​ student's final exam score drops ___ points, on average. The average final exam score of students who miss no classes is ___?

C) Predict the final exam score for a student who misses five class periods.

D) R= ___?

E) Critical value = ____?

F) Compute the residual.

Answer 1

We can get regression output from excel .

Data tab > data analysis > regression Also tick in to the residuals check box.

So we get :

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.942391
R Square	0.8881
Adjusted R Square	0.874113
Standard Error	3.291882
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	688.0371	688.0371	63.49265	4.49E-05
Residual	8	86.69188	10.83648
Total	9	774.729
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	89.28545	1.934816	46.14674	5.37E-11	84.82376	93.74715
Number of absences (X)	-2.88788	0.362424	-7.96823	4.49E-05	-3.72363	-2.05213

The intercept = a = 89.29 , b = slope = -2.89

The regression equation is

B. Here slope = -2.89.

So we interpret it as , if number of absences increases by 1, final exam score will decrease by 2.89 points.

For every additional​ absence, a​ student's final exam score drops _2.89__ points, on average.

Intercept = 89.29

If number of absences is 0, final exam score will be 89.29 points.

The average final exam score of students who miss no classes is 89.29 points.

c)

x = 5

= 74.84

d) From output we get :

R = 0.94

e) Here n = 10,

so the critical value for correlation coefficient = 0.632.

f) The residual = e = y -

Observation	y	Predicted Final exam score ()	Residuals
1	89.4	89.28545	0.114545
2	87.2	86.39758	0.802424
3	84.5	83.5097	0.990303
4	81.7	80.62182	1.078182
5	77.3	77.73394	-0.43394
6	74.8	74.84606	-0.04606
7	63.7	71.95818	-8.25818
8	72.1	69.0703	3.029697
9	66.4	66.18242	0.217576
10	65.8	63.29455	2.505455