Applied Regression Analysis Quiz: Minitab Output Results for: GASOLINE_MILEAGE_D
ID: 3201288 • Letter: A
Question
Applied Regression Analysis Quiz: Minitab Output
Results for: GASOLINE_MILEAGE_DATA_WITH_INDICATOR_VARIABLES.MTW
y: miles per gallon
x1: Displacement (cubic inches)
x2: Horsepower (ft-lb)
x3: Torque (ft-lb)
Etc.
Regression Analysis: y versus x1, x2, x3, x4, x5, x6, x7, x8, x9, x10
The regression equation is
y = 19.4 - 0.0761 x1 - 0.0743 x2 + 0.121 x3 + 1.32 x4 + 5.98 x5 + 0.29 x6
- 3.40 x7 + 0.185 x8 - 0.409 x9 - 0.00518 x10
30 cases used, 2 cases contain missing values
Predictor Coef SE Coef T P
Constant 19.35 28.99 0.67 0.512
x1 -0.07613 0.05623 -1.35 0.192
x2 -0.07425 0.08663 -0.86 0.402
x3 0.12098 0.08907 1.36 0.190
x4 1.317 3.021 0.44 0.668
x5 5.976 3.076 1.94 0.067
x6 0.289 1.251 0.23 0.820
x7 -3.398 2.859 -1.19 0.249
x8 0.1853 0.1259 1.47 0.158
x9 -0.4094 0.3124 -1.31 0.206
x10 -0.005184 0.005742 -0.90 0.378
S = 3.14565 R-Sq = 83.5% R-Sq(adj) = 74.8%
Analysis of Variance
Source DF SS MS F P
Regression 10 951.098 95.110 9.61 0.000
Residual Error 19 188.007 9.895
Total 29 1139.105
Source DF Seq SS
x1 1 866.227
x2 1 5.436
x3 1 4.441
x4 1 14.489
x5 1 2.876
x6 1 9.074
x7 1 6.644
x8 1 0.347
x9 1 33.502
x10 1 8.063
Unusual Observations
Obs x1 y Fit SE Fit Residual St Resid
22 360 21.470 16.170 2.212 5.300 2.37R
31 360 13.770 19.049 2.080 -5.279 -2.24R
R denotes an observation with a large standardized residual.
Questions:
QUESTION 11
What are the units of the slope estimate beta 1 hat?
a) miles per gallon
b) cubic inches
c) miles per gallon per cubic inch
d) 1/(cubic inches)
QUESTION 12
A one-unit change in x1 changes the estimated mean of y by how much?
a) an increase of 0.0761
b) a decrease of 0.0761
c) an increase of 19.4
d) cannot be determined from the output
QUESTION 13
What is the estimated sigma ?
a) 3.146
b) 9.895
c) 9.752
d) 95.11
QUESTION 14
Calculate a 95% confidence interval for beta 1.
a) (-0.13236, -0.0199)
b) (-0.1938, 0.0416)
c) (-0.24482, 0.09256)
d) Not available
QUESTION 15
In the output, no t-tests are significant at
alpha =0.05, but the F-test for regression has a p-value of approximately 0. The best explanation of these results is:
a) These regressors are not useful predictors
b) Multicollinearity is present
c) All these regressors are useful predictors
d) Only first variable x1 is a useful predictor
Explanation / Answer
Question 11) Cubic inches
Question 12) a decrease of 0.0761
Question 13) S = 3.14565
Question 14) d) Not available
Question 15) All these regressors are useful predictors
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