Question

Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub-Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics.

Variable	Coefficient			Standard Error		t Statistic
Intercept		5.4800		0.12454			44.00
Sale price		−0.0749		0.0222			−3.37
Sub-Zero brand		1.1350		0.1387			8.18
Total capacity (in cubic ft)		0.07689		0.00608			12.64
Two-door, freezer on bottom		0.04725		0.07467			0.63
Two-door, side freezer		Base
Two-door, freezer on top		−0.3753		0.03813			−9.84
One door with freezer		−0.7522		0.1288			−5.84
One door, no freezer		−0.8762		0.1362			−6.43

(a) Write the regression model, being careful to exclude the base indicator variable. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)

ln(Price) = ______ + ______ SalePrice +______  Sub-Zero ______+  Capacity + ______ 2DoorFzBot ______+ _______2DoorFzTop _____+ ______ 1DoorFz + _______ 1DoorNoFz

(b) Find the p-value for each coefficient, using 314 degrees of freedom. Using an α = .05, which predictor variable(s) are not significant predictors? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.)

	p-value
SalePrice
Sub-Zero
Capacity
2DoorFzBot
2DoorFzTop
1DoorFz
1DoorNoFz

(c) By how much does the natural log of refrigerator price decrease from a two-door, side freezer model to a two-door, top freezer model? (Round your answer to 4 decimal places.)

The natural log of the price decreases by            

Answer 1

a.

Regression equation:

ln(Price) = 5.48 - 0.0749 SalePrice + 1.1350 Sub-Zero  + 0.07689  Capacity + 0.04725  2DoorFzBot - 0.3753  2DoorFzTop - 0.7522  1DoorFz - 0.8762 1DoorNoFz

b.

	p-value
SalePrice	0.000845477
Sub-Zero	7.1281E-15
Capacity	6.92486E-30
2DoorFzBot	0.529152754
2DoorFzTop	4.32854E-20
1DoorFz	1.30332E-08
1DoorNoFz	4.74522E-10

P-value is obtained using excel with function =TDIST(test statistic, df, tails). Note that enter absolute value of test statistic.

c.

The natural log of the price decreased by the 0.3753