Question 4 Find the estimated nultiple linear regression equation for predicting
ID: 3238985 • Letter: Q
Question
Question 4
Find the estimated nultiple linear regression equation for predicting "risk" based on the person's "pressure" and wheter they are a "smoker". WHat is the r square value as a decimal? Round to three places of decimal..
Risk Age Pressure Smoker 12 57 152 No 24 67 163 No 13 58 155 No 56 86 177 Yes 28 59 196 No 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 37 59 207 YesExplanation / Answer
Let,
Y = Risk
X1 = Pressure
X2 = Smoker (Yes = 1, No = 0)
Y
X1
X2
12
152
0
24
163
0
13
155
0
56
177
1
28
196
0
51
189
1
18
155
1
31
120
0
37
135
1
15
98
0
22
152
0
36
173
1
15
135
1
48
209
1
15
199
0
36
119
1
8
166
0
34
125
1
3
117
0
37
207
1
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.735
R Square
0.541
Adjusted R Square
0.487
Standard Error
10.641
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
2
2265.897427
1132.9487
10.005
0.0013
Residual
17
1925.052573
113.23839
Total
19
4190.95
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-2.427
11.99979785
-0.2022405
0.842129
-27.7442058
22.89051456
Pressure
0.129
0.075878151
1.6952884
0.108257
-0.03145356
0.288724249
Smoker
18.336
4.826446863
3.7991644
0.001433
8.15355264
28.51937801
The multiple regression equation is:
y^ = -2.427 + 0.129x1 + 18.336x2
R-square = 0.541
Y
X1
X2
12
152
0
24
163
0
13
155
0
56
177
1
28
196
0
51
189
1
18
155
1
31
120
0
37
135
1
15
98
0
22
152
0
36
173
1
15
135
1
48
209
1
15
199
0
36
119
1
8
166
0
34
125
1
3
117
0
37
207
1
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