Table 2 presents the highway mileage \"MPG\" and engine displacement \"Engine In
ID: 3054251 • Letter: T
Question
Table 2 presents the highway mileage "MPG" and engine displacement "Engine In3" for Chrysler vehicles from 2005 (U.S. EPA). Calculate the ordinary least squares estimates of the slope and intercept and graph the regression mode 8 8 (b) Give an interpretation of the slope and intercept. 2 (c) Obtain the fitted value and the corresponding residual for the Neon with an engine displacement of 122 cubic inches, 1 Yds 1 Rating 2 Engine In3 2 MPG 3 Compress 3 Density CROSSFIRE ROADSTER DAKOTA PICKUP 4WD GRAND CHEROKEE 2WD GRAND CHEROKEE 4WD LIBERTY/CHEROKEE 2WD LIBERTYICHEROKEE 4WD NEON/SRT-4/SX 2.0 RAM 1500 PICKUP 2WD RAM 1500 PICKUP 4WD TOWN & COUNTRY 2WD VIPER CONVERTIBLEExplanation / Answer
Here dependent variable is MPG and independent variable is Engine ln3.
The dataset is of 21 observations.
We have to fit here simple linear regression.
We can fit regression in excel.
steps :
ENTER data into excel sheet --> Data --> Data Analysis --> Regression --> ok --> Input Y range : select mpg data --> Input X range : Engine ln3 data --> Click on labels --> Output range : select one empty cell --> ok
The regression equation is,
y = 39.16 - 0.04*x
where intercept = 39.16
slope = -0.04
b) Interpretation :
Intercept : If x = 0 then y will be 39.16
slope :
One unit change in x will be 0.04 unit decrease in y.
c) Now we have to predict y when x = 122 cubic inches.
This we can find using regression equation.
y^ = 39.16 - 0.04 * 122 = 34.25
Now residual = observed - expected = y - y^
In the data for x = 122 y will be 41.3.
Residual = 41.3 - 34.25 = 7.05
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