# Statistics

posted by
**Kris**
.

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

Adjusted R-Squared = 0.877997

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.