A consumer organization has reported test data for 50 car models. We will examin
ID: 3231629 • Letter: A
Question
A consumer organization has reported test data for 50 car models. We will examine the association between X = the weight of the car (in thousands of pounds) and Y = the fuel efficiency (in miles per gallon). Use the data provided in the following regression to answer the questions.
A. Find and interpret the y-intercept and slope.
B. Find the Coefficient of Determination R2 in the regression and interpret its value.
C. Find the Correlation Coefficient r in Excel and interpret its value. Discuss the strength and direction of the relationship between weight and mileage.
D. Test the Ha (alternative hypothesis) that there is a linear relationship between weight and mileage. Be sure to include the hypotheses, p-value, and conclusion. Explain your answer in the context of the given situation.
E. Estimate the mean Y (mileage) when the weight X=4 (4000 lbs) with a 95% confidence intereval. Interpret your result in the context of the given situation.
F. Estimate the new Y (mileage) when the weight X=4 (4000 lbs) with a 95% confidence intereval. Interpret your result in the context of the given situation.
SUMMARY OUTPUT Regression Statistics Multiple R 0.86938497 R Square 0.755830225 Adjusted R Square 0.750743355 Standard Error 2.413372073 Observations ANOVA. Significance df MS 1 865.4104913 865.4104913 148.5845283 2.64051E-16 Regression 48 279.5695087 5.824364764 Residual 1144.98 Total 49 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% t Stat Coefficients Error 48.73930527 1.97558114 24.67086989 6.43583 E-29 44.76713316 52.71147737 44.76713 316 52.71 147 737 Intercept 8.21362465 0.673826454 12.189525 35 2.64051E-16 9.56844354 6.85880576 9.56844354 6.85880576 X Variable 1Explanation / Answer
a) Intercept = 48.73930527 If the weight of the car is zero the fuel efficiency is 48.7393. it is meaning less
Slope = -8.21362465, If the weight of the car increases 1 thousands pounds the fuel effeciency decrease 8.136 miles per gallon
b) R2=0.7558. i.e. 75.58% of variations in the fuel efficiency can be explained by the weight of the car
c)
Correlation Coefficient r = sqrt(0.7558) = 0.8694
d)
The p-value of the regression is 0.0000 which is less than alpha 0.05, so we reject H0
Thus we conclude that there is a linear relationship between weight and mileage
e) Given weight X=4
Mean y = 48.73930527 - 8.21362465 (4) = 45.26183
f)
Given weight X=4
Mean y = 48.73930527 - 8.21362465 (4) = 45.26183
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.