Question

The data set contains 86 domestic beer brands with the percent alcohol, carbohydrates (in grams), and calories per 12 ounces. Round answers to 4 decimal places.

Simple linear regression results:

Dependent Variable: Calories
Independent Variable: Carbohydrates
Calories = 82.659903 + 5.2765795 Carbohydrates
Sample size: 86
R (correlation coefficient) = 0.80319062
R-sq = 0.64511518
Estimate of error standard deviation: 16.6542

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	82.659903	5.0556247	≠ 0	84	16.350087	<0.0001
Slope	5.2765795	0.42700988	≠ 0	84	12.357043	<0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	42352.269	42352.269	152.69651	<0.0001
Error	84	23298.44	277.36238
Total	85	65650.709

1. Find the value of the correlation coefficient between carbohydrates and calories. Would you describe the linear relation as weak, moderate, or strong?
2. Find the intercept of the least-squares regression line to predict the calories given the carbo- hydrates.
3. Find the slope of the least-squares regression line to predict the calories given the carbohy- drates.
4. Write the equation of the least-squares regression line to predict the calories given the carbo- hydrates.
5. If a 12 ounce beer has 15 grams of carbohydrates, on average what will the calories content be?

Answer 1

a) the correlation coefficient between carbohydrates and calories

R (correlation coefficient) = 0.80319062 and it is relationship is strong and linear.

b) Intercept of the least-squares regression line to predict the calories given the carbo- hydrates.

Ans : 82.659903

c)The slope of the least-squares regression line to predict the calories given the carbohy- drates

Ans: 5.2765795

d) Write the equation of the least-squares regression line to predict the calories given the carbo- hydrates

Carbohydrates Calories = 82.659903 + 5.2765795 Carbohydrates

e) If a 12 ounce beer has 15 grams of carbohydrates, on average what will the calories content be?

We have

Carbohydrates Calories = 82.659903 + 5.2765795 Carbohydrates

So If a 12 ounce beer has 15 grams of carbohydrates then

Carbohydrates Calories = 82.659903 + 5.2765795*15

Carbohydrates Calories = 161.8086