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Is the number of calories in a beer related to the number of carbohydrates? and/or the...

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Basic Math

Is the number of calories in a beer related to the number ofcarbohydrates? and/or the percentage of alcohol in the? beer? Theaccompanying table has data for 35 beers. The values for threevariables are? included: the number of calories per 12? ounces, thealcohol? percentage, and the number of carbohydrates? (in grams)per 12 ounces. Complete parts a through d.

CaloriesAlcohol%Carbohydrates
1104.26.6
700.413.3
1104.27
552.41.9
1104.27
642.82.4
1164.28
1143.88.3
1354.211.5
1103.98.3
944.12.6
954.12.6
954.13.2
1034.15
1034.15.5
1104.17
1244.19.7
994.33.1
1104.17.4
1134.36.7
1054.25.7
1284.311.4
954.23.2
1384.312.5
964.23.2
1114.45.8
1746.111.1
1796.410.6
1816.510.6
1886.512.7
2006.617
2156.719.3
2146.819.4
2316.920
200718

Perform a multiple linear regression? analysis, using caloriesas the dependent variable and percentage alcohol and number ofcarbohydrates as the independent variables.

Let

Upper X 1X1

represent alcohol percentage and let

Upper X 2X2

represent the number of carbohydrates.

ModifyingAbove Upper Y with caret equals nothing plus leftparenthesis nothing right parenthesis Upper X 1 plus leftparenthesis nothing right parenthesis Upper X 2

Answer & Explanation Solved by verified expert
4.1 Ratings (483 Votes)

We will do this problem with the help of Excel.

Load the data into Excel.

Go to Data>Megastat.

Select the option Correlation/Regression and go to Regression.

Select percentage alcohol and number of carbohydrates? as the independent variable(s), x.

Select calories as the dependent variable, y.

Click OK.

The output will be as follows:

R² 0.991
Adjusted R² 0.990 n   35
R   0.995 k   2
Std. Error   4.507 Dep. Var. Calories
ANOVA table
Source SS   df   MS F p-value
Regression 70,230.6558 2   35,115.3279 1728.98 2.50E-33
Residual 649.9156 32   20.3099
Total 70,880.5714 34  
Regression output confidence interval
variables coefficients std. error    t (df=32) p-value 95% lower 95% upper
Intercept -0.1426
Alcohol% 19.8187 0.7047 28.125 3.89E-24 18.3834 21.2541
Carbohydrates 4.2690 0.1895 22.526 3.39E-21 3.8830 4.6550

Therefore, our regression equation is:

Calories = -0.1426 + 19.8187*Alcohol(%) + 4.2690*Carbohydrates

Or

y = -0.1426 + 19.8187*x1 + 4.2690*x2

where x1 = Alcohol(%)

x2 = Carbohydrates

Thus, the above output is the result of the multiple linear regression.
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