# Statistics

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Simple Linear Regression Analysis

2. Weight of Car: Miles gallon – Do heavier cars really use more gasoline? The following data were obtained from Consumer Reports (Vol 62 no. 4). Weight of car is in hundreds of pounds.

Car Weight 27 44 32 47 23 40 34 52
MPG 30 19 24 13 29 17 21 14

A simple linear regression of the model MPG = b + b WEIGHT
The results are shown below:

MPG & CAR WEIGHT
REGRESSION FUNCTION & ANOVA FOR MPG

MPG = 43.32625 - 0.600702 WEIGHT

R-Squared = 0.895426
Standard error of estimate = 2.236055
Number of cases used = 8

Analysis of Variance
p-value
Source SS df MS F Value Sig Prob
Regression 256.87 1 256.87 51.37567 0.000372
Residual 29.99 6 4.99
Total 286.875 7

MPG & CAR WEIGHT
REGRESSION COEFFICIENTS FOR MPG

Two-Sided p-value
Variable Coefficient Std Error t Value Sig Prob
Constant 43.32625 3.23051 13.41156 0.000011
WEIGHT -0.60070 0.08381 -7.16768 0.000372 *

Standard error of estimate = 2.236055
Durbin-Watson statistic = 0.995097

(a) What is the estimated simple linear regression?
(b) What sort of relationship exists between MPG and car weight? Does the relationship make sense to you? Why or why not?
(c) Interpret the R-square in the computer output.
(d) Estimate the MPG for a car that weighs 20 hundred pounds and a car that weight 60 hundred pounds.

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