A psychologist conducted an experiment analysing therelationship between student scores in an exam and the amount ofattention they paid in class. The latter was measured using a typeof brain monitor. The Psychologist believed that scores wouldincrease by 1 for every two unit increase in attention. The dataare listed in the excel spreadsheet.

Estimate a linear regression between the score (Y) and themeasure of attention(X).

(a) Write out the equation for Y in the form , but withcoefficients. Show the estimated standard errors in parenthesisbelow the coefficients. What is the R2 of the regression? Calculatea 99 percent confidence interval forβ.                                                               [5pts]

(b) What are the mean and the estimated standard deviation ofthe estimated residuals? [2 pts]

Hint: the first answer is definitional and the second answer iseasily seen from the output.

(c )Test the hypothesis that there is no relationship betweenthe variables at the 90 percent significancelevel.                                                                                                    [3pts]

(d) Test the hypothesis that the coefficient β=0.5 at the 99%significancelevel.               [3pts]

(e) The Psychologist concluded from the experiment that testscores increase significantly if students pay attention in class.In one word, how would you describe the results of thisexperiment based on the data youhave?                                                                                                       [2pts]

DATA:

Regression data for Psychology Experiment
Attention	Score
18	80
35	90
86	80
22	50
72	76
102	74
86	75
30	80
35	85
94	82
16	80
42	41
50	50
96	96
60	80
106	70
80	65
14	14
11	14
80	85
12	14
37	43
26	80
86	70
5	20
17	20
35	80
76	68
50	70
15	16
90	86
96	80
7	16
10	14
35	65
88	88
20	32
22	70
50	65
22	62
35	50
64	92
68	84
13	15
102	102
86	85
18	24
78	64
98	78
70	80
60	70
98	98
9	14
50	90
104	72
35	45
60	60
74	72
88	88
80	95
22	58
8	14
86	110
60	75
92	84
60	100
80	75
86	95
16	18
86	90
35	75
35	60
80	60
80	70
104	104
80	100
60	90
86	100
62	96
60	65
39	41
50	80
50	75
6	18
60	95
22	54
21	40
100	100
94	94
80	90
48	41
106	106
50	43
46	41
90	90
60	85
92	92
22	80
35	70
66	88
80	60
50	60
80	80
100	76
50	45
86	65
19	28
50	85
22	75
86	105