Question

In: Statistics and Probability

A study tried to relate the number of calories in beer to the percentage of alcohol...

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. Then answer parts​ (a) through​ (f). a. State the regression equation, Fstat, and critical value

how do you find each variable in the regression equation? please show steps in excel.

Calories (Y) Alcohol % (X1) Carbohydrates (X2)
94 4.1 3.2
153 4.8 12.5
147 5.4 8.8
144 4.9 10.6
168 5.8 12.5
174 6.2 11.1
147 4.5 13.4
147 4.8 13.9
149 5.5 9.8
109 4.1 7.2
143 5.8 6.6
152 4.7 13.8
104 4.1 5.7
144 4.5 12.9
151 4.6 14.1
112 4.2 6.7
143 4.7 13.1
109 4.1 6.9
98 4.4 3.4
113 3.7 8.2
146 4.7 11.8
179 5.7 14.2
159 4.7 17.9
159 4.9 19.9
165 5.2 16.9
162 4.8 19.6

Solutions

Expert Solution

Excel Goto Data > Data analysis > Regression > select y and then in x select both x1 and x2

> ok

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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9761
R Square 0.9527
Adjusted R Square 0.9486
Standard Error 5.4806
Observations 26
ANOVA
df SS MS F Significance F
Regression 2 13923.17641 6961.58821 231.76339 5.72984E-16
Residual 23 690.8620476 30.0374803
Total 25 14614.03846
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -4.8713 8.5026 -0.5729 0.5723 -22.4602 12.7177 -22.4602 12.7177
Alcohol % (X1) 22.5361 1.8404 12.2450 0.0000 18.7289 26.3434 18.7289 26.3434
Carbohydrates (X2) 3.3352 0.2525 13.2063 0.0000 2.8128 3.8577 2.8128 3.8577

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Regression equation

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Fstat = 231.76339

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Fcrit = F.INV.RT(0.05,2,23) = 3.4221

==================================

x1= It is positive and statistically significant , because p-value is less than 0.05

same for x2


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