Question

Fat (g)   Calories
10.9   445
11.2   486
11.5   492
11.6   506
11.7   492
13.1   536
15.2   551

​b) Interpret the value of Upper R2 in this context.

A. 7.7​% of the deviation in the number of calories can be explained by the deviation in the number of grams of fat in a​ fast-food burger.

B.The number of calories in a​ fast-food burger can be explained by 77.7​% of the number of grams of fat.

C. 77.7​% of the number of calories can be explained by the number of grams of fat in a​ fast-food burger.

D. 77.7​% of the variability in the number of calories can be explained by the variability in the number of grams of fat in a​ fast-food burger.

​c) Write the equation of the line of regression. Choose the correct equation below.

A. ModifyingAbove y with caretyequals=253.020253.020plus+20.38620.386x

B. ModifyingAbove x with caretxequals=253.020253.020plus+20.38620.386y

C. ModifyingAbove y with caretyequals=253.020253.020xplus+20.38620.386

D. ModifyingAbove x with caretxequals=253.020253.020yplus+20.38620.386

​d) Use the residuals plot to explain whether your linear model is appropriate.

A. The residuals plot shows no pattern. The linear model appears to be appropriate.

B. The residuals plot shows a curved pattern. The linear model is inappropriate.

C. The residuals increase in magnitude as the value of the independent variable increases. The linear model is inappropriate.

D. The residuals sum to zero. The linear model appears to be appropriate.

​e) Explain the meaning of the​ y-intercept of the line.

A.The model predicts that a​ zero-calorie burger would have 253.020 grams of fat.

B.The model predicts that a​ zero-calorie burger would have 20.386 grams of fat.

C.The model predicts that a​ fat-free burger would have 253.020 calories.

D.The model predicts that a​ fat-free burger would have 20.386 calories.

​f) Explain the meaning of the slope of the line.

A.For each additional gram of​ fat, the model predicts an increase of 253.020 calories.

B.For each additional gram of​ fat, the model predicts an increase of 20.386 calories.

C.For each additional​ calorie, the model predicts an increase of 20.386 grams of fat.

D.For each additional​ calorie, the model predicts an increase of 253.020 grams of fat.

​g) A new burger containing 15 grams of fat is introduced. According to this​ model, its residual for calories is −26.172.

How many calories does the burger​ have?

The burger has _____ calories.

Answer 1

​b) Interpret the value of Upper R2 in this context.

Answer:

D. 77.7​% of the variability in the number of calories can be explained by the variability in the number of grams of fat in a​ fast-food burger.

​c) Write the equation of the line of regression. Choose the correct equation below.

Answer:

A. ModifyingAbove y with caretyequals=253.020253.020plus+20.38620.386x

​d) Use the residuals plot to explain whether your linear model is appropriate.

A. The residuals plot shows no pattern. The linear model appears to be appropriate.

​e) Explain the meaning of the​ y-intercept of the line.

Answer:

C.The model predicts that a​ fat-free burger would have 253.020 calories.

​f) Explain the meaning of the slope of the line.

Answer:

B.For each additional gram of​ fat, the model predicts an increase of 20.386 calories.

Our result are based on below data and model using excel

Fat = x	Calaries = y
10.9	445
11.2	486
11.5	492
11.6	506
11.7	492
13.1	536
15.2	551

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.881354
R Square	0.776786
Adjusted R Square	0.732143
Standard Error	18.01892
Observations	7

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	253.0202	59.8715	4.226054	0.00828	99.11559	406.9248	99.11559	406.9248
Fat	20.38567	4.887091	4.171329	0.008728	7.822998	32.94833	7.822998	32.94833