Question

Data for age (in years) and price (in hundreds of dollars) for a particular brand of car are provided in the accompanying data table. Presume that the assumptions for regression inferences have been met. Complete parts (a) through (d) below using the given data.

X (age) 6, 6, 6, 2, 2, 5, 4, 5, 1, 4

Y (price) 289, 280, 293, 428, 382, 315, 355, 326, 423, 322

A) Obtain a point estimate for the mean price of all 3-year old cars of this brand.

B) Determine a 90% confidence interval for the mean price of all 3-year old cars of this brand.

C) Find the predicted price of a 3-year old car of this brand.

D) Determine a 90% prediction interval for the price of a 3-year old car of this brand.

Answer 1

A. Point estimate for the mean price of all 3-year old cars of this brand=456.11-28.003*3=$37210.

B. 90% confidence interval for the mean price of all 3-year old cars of this brand: ($36133, $38287)

C. Predicted price of a 3-year old car of this brand=$37210.

D. 90% prediction interval for the price of a 3-year old car of this brand: ($34129, $40292)

Minitab output:

Regression Analysis: Y versus X

The regression equation is
Y = 456 - 28.0 X

Predictor     Coef    SE Coef       T      P
Constant    456.11    12.46   36.60 0.000
X              -28.003    2.793   -10.02 0.000

S = 15.5278   R-Sq = 92.6%   R-Sq(adj) = 91.7%

Analysis of Variance

Source          DF     SS     MS       F      P
Regression       1 24231 24231 100.50 0.000
Residual Error   8   1929    241
Total                  9 26160

Predicted Values for New Observations

New Obs     Fit      SE Fit       90% CI            90% PI
      1        372.10    5.79 (361.33, 382.87) (341.29, 402.92)

Values of Predictors for New Observations

New Obs     X
      1        3.00