Use the wine data in the Excel folder to estimate the parameters of the multiple
ID: 3324578 • Letter: U
Question
Use the wine data in the Excel folder to estimate the parameters of the multiple regression model: y=a+31x1 +32x2 + where y = deaths/ 100,000, = heart desease, and x, = liver disease. a. Report all estimates, including s2, the standard error of the regression. Test the hypotheses that i) 31 = 0 vs. 31 > 0, and ii) 32-0 vs. 32 > 0 at a = .05. Would your conclusion change for ii (liver) if the hypotheses were 32-0 vs. 32 0? c. Report R2, and interpret its value. Using your regression estimates, predict the death rate for a country with liver-6 and heart 2. d. Extra Credit: what is a 90% confidence interval for 31?Explanation / Answer
Result:
a). s2 = 3431.2138
s=58.577
b). for
H0: 1 =0, H1: 1 >0
Calculated t=5.838, P=0.0000 which is < o.o5 level. 1 is significant.
( p value for upper tail test is half of the two tailed test given uin the output).
H0: 2 =0, H1: 2 >0
Calculated t= 2.403, P=.0273/2 =0.0136 ( one sided p value ) which is < o.o5 level. 2 is significant.
H0: 2 =0, H1: 2 0
Calculated t= 2.403, P=.0273 which is < o.o5 level. 2 is significant.
The result is same.
R square =0.669
66.9% of variance in deaths is explained by the regression model.
The regression line is death 517.5400+1.3229*heart+3.3303*liver
Predicted death when heart=2 and liver=6 is
=517.5400+1.3229*2+3.3303*6
=540.1676
90% CI for 1 is (0.9300, 1.7157).
Regression Analysis
R²
0.669
Adjusted R²
0.632
n
21
R
0.818
k
2
Std. Error
58.577
Dep. Var.
death
ANOVA table
Source
SS
df
MS
F
p-value
Regression
124,555.1046
2
62,277.5523
18.15
0.0000
Residual
61,761.8478
18
3,431.2138
Total
186,316.9524
20
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
90% lower
90% upper
Intercept
517.5400
64.9769
7.965
0.0000
404.8658
630.2141
heart
1.3229
0.2266
5.838
0.0000
0.9300
1.7157
liver
3.3303
1.3861
2.403
.0273
0.9267
5.7339
Regression Analysis
R²
0.669
Adjusted R²
0.632
n
21
R
0.818
k
2
Std. Error
58.577
Dep. Var.
death
ANOVA table
Source
SS
df
MS
F
p-value
Regression
124,555.1046
2
62,277.5523
18.15
0.0000
Residual
61,761.8478
18
3,431.2138
Total
186,316.9524
20
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
90% lower
90% upper
Intercept
517.5400
64.9769
7.965
0.0000
404.8658
630.2141
heart
1.3229
0.2266
5.838
0.0000
0.9300
1.7157
liver
3.3303
1.3861
2.403
.0273
0.9267
5.7339
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