A study tried to relate the number of calories in beer to the percentage of alco
ID: 3225569 • Letter: A
Question
A study tried to relate the number of calories in beer to the percentage of alcohol and number of carbohydrates. Use the accompanying data table to perform a natural logarithmic transformation of the dependent variable (calories). Using the transformed dependent variable and the percentage of alcohol and the number of carbohydrates as the independent variables, perform a multiple regression analysis.
a. State the regression equation.
ln Y^t i= ___ + ___X1i + ___X2i
(Round to five decimal places as needed.)
Calories (Y) Alcohol % (X1) Carbohydrates (X2)
95 4.2 3.2
152 4.8 12.5
148 5.5 8.9
145 4.9 10.5
168 5.9 12.5
174 6.2 11.1
148 4.5 13.4
148 4.9 13.9
148 5.5 9.7
109 4.1 7.2
143 5.9 6.6
152 4.6 13.8
105 4.1 5.6
144 4.6 12.9
152 4.7 14.1
113 4.2 6.7
142 4.7 13.1
109 4.2 6.9
98 4.4 3.5
114 3.8 8.2
145 4.6 11.9
179 5.8 14.2
159 4.7 17.9
159 4.9 19.8
166 5.1 16.8
162 4.8 19.7
Explanation / Answer
From Excel
The regression equation
y=a+bx1+cx2
from Excel
y= -2.94 +21.84(Alcohol) +3.43(3.43)
SUMMARY OUTPUT Regression Statistics Multiple R 0.975146 R Square 0.950909 Adjusted R Square 0.94664 Standard Error 5.543615 Observations 26 ANOVA df SS MS F Significance F Regression 2 13691.52 6845.759 222.7591 8.84E-16 Residual 23 706.8283 30.73167 Total 25 14398.35 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -2.9433 8.587895 -0.34273 0.734916 -20.7087 14.82211 -20.7087 14.82211 Alcohol 21.8392 1.8281 11.94639 2.42E-11 18.05749 25.62091 18.05749 25.62091 carbo 3.430151 0.253346 13.53939 1.92E-12 2.906065 3.954237 2.906065 3.954237Related Questions
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