Question

Studies have shown that exercising can help prevent heart disease. Within reasonable limits, the more you exercise, the less risk you have of suffering from heart disease. One way in which exercise reduces your risk is by reducing serum cholesterol. The more you exercise, the lower your cholesterol concentration. It has recently been shown that the amount of time you spend watching TV, an indicator of a sedentary lifestyle, might be a good predictor of heart disease; that is, the more TV you watch, the greater your risk of heart disease. As a result, a research team is trying to determine if cholesterol concentration is related to time spent watching television in otherwise healthy 45 to 65-year-old men. They believed that there would be a positive relationship: the more time people spent watching TV, the greater their cholesterol concentration. The researcher also wished to be able to predict cholesterol concentration and to know the proportion of cholesterol concentration that time spent watching TV could explain. The data the researchers collected can be downloaded in Canvas and is called cholesterol and screen time. I want to use SPSS to test whether the researchers’ predictions are true and to determine the proportion of cholesterol concentration that is explained by time watching. I've provided the data set.

case number

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
92
93
94
95
96
97
98
99
100

TINE WATCHING TV

168
170
170
164
159
168
165
156
172
170
165
168
171
168
166
167
163
161
168
170
171
165
162
175
169
170
176
179
173
176
170
172
175
172
173
177
170
171
173
170
163
173
169
170
171
174
178
174
176
176
171
176
176
172
173
176
172
171
173
176
171
182
180
183
170
176
182
174
178
176
169
172
176
175
170
177
180
176
171
183
177
169
167
171
170
174
170
170
173
173
177
168
179
163
179
168
170
171
171

CHOLESTROL

4.60
4.80
5.39
5.16
5.09
5.70
5.25
4.89
4.90
4.68
4.77
4.65
5.61
4.81
5.64
6.16
5.35
4.65
5.79
4.80
5.05
5.66
4.63
5.01
5.56
6.41
5.03
5.35
5.09
5.99
4.72
4.70
5.01
5.25
5.83
6.06
6.10
5.27
5.54
5.84
5.01
6.04
4.69
5.43
5.71
6.41
5.26
5.61
6.11
5.25
5.53
6.55
5.25
5.55
5.50
5.23
5.12
6.27
5.31
5.10
5.12
5.91
5.91
6.33
4.99
5.10
5.56
5.27
5.60
4.87
5.73
4.58
5.22
5.13
5.68
6.21
6.21
5.99
4.57
5.66
5.23
5.82
6.14
4.80
5.23
5.91
6.21
4.65
5.56
5.16
5.65
5.30
6.00
5.48
6.43
4.36
5.17
5.52
6.10

Answer 1

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.3594
R Square	0.1292
Adjusted R Square	0.1202
Standard Error	0.4906
Observations	99
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3.4622	3.4622	14.3856	0.0003
Residual	97	23.3454	0.2407
Total	98	26.8077
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.9365	1.6753	-0.5590	0.5774	-4.2616	2.3885
X	0.0370	0.0097	3.7928	0.0003	0.0176	0.0563

y^ = -0.9365 + 0.0370*x

we want to test

= 0

0

p-value = 0.0003/2 = 0.0001 { as this is one-tailed test}

since p-value < alpha

we reject the null hypothesis

we conclude that there is a positive relationship

the proportion of cholesterol concentration that is explained by time watching = R^2 = 0.1292

= 12.92%