Suppose a certain retailer sells several models of refrigerators. A random sample of the models sold by this retailer and their corresponding cubic feet (cu. ft.) and list price can be found below.

Model Cu. Ft. List Price

Model 1 18.3 $899.99

Model 2 24.8 $1,799.99

Model 3
with Thru-the-Door Ice and Water 25.4 $1,799.99

Model 4 19.3 $749.99

Model 5 17.3 $599.99

Model 6
with Thru-the-Door Ice and Water 19.6 $1,619.99

Model 7 25.0 $999.99

Model 8 24.5 $1,299.99

Model 9
with Thru-the-Door Ice and Water 25.4 $1,299.99

Model 10
with Thru-the-Door Ice and Water 26.0 $1,299.99

Model 11
with Thru-the-Door Ice and Water 25.6 $1,099.99

Model 12 18.0 $679.99

Model 13
with Thru-the-Door Ice and Water 25.0 $2,199.99

Model 14 20.8 $849.99

Model 15 15.5 $549.99

Model 16
with Thru-the-Door Ice and Water 28.2 $2,599.99

Model 17 27.8 $2,999.99

Model 18
with Thru-the-Door Ice and Water 26.6 $2,399.99

Model 19
with Thru-the-Door Ice and Water 22.6 $1,099.99

Model 20
with Thru-the-Door Ice and Water 21.8 $1,499.99

Model 21 20.9 $1,669.99

(a)

Develop the estimated simple linear regression equation to show how list price is related to the independent variable cubic feet. (Round your numerical values to four decimal places. Let
x₁
represent the cubic feet and y represent the list price.)

ŷ =

(b)

At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between list price and cubic feet.

State the null and alternative hypotheses.

H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₁ ≤ 0
H_a: β₁ > 0    H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ = 0
H_a: β₁ > 0

Find the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

State your conclusion.

Reject H₀. There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.Reject H₀. There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet.    Do not reject H₀. There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.Do not reject H₀. There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet.

(c)

Develop a dummy variable that will account for whether the refrigerator has the thru-the-door ice and water feature. Code the dummy variable with a value of 1 if the refrigerator has the thru-the-door ice and water feature and with 0 otherwise. Use this dummy variable to develop the estimated multiple regression equation to show how list price is related to cubic feet and the thru-the-door ice and water feature. (Round your numerical values to four decimal places. Let
x₁
represent the cubic feet,
x₂
represent whether the refrigerator has the thru-the-door ice and water feature, and y represent the list price.)

ŷ =

(d)

At ? = 0.05, is the thru-the-door ice and water feature a significant factor in the list price of a refrigerator?

State the null and alternative hypotheses.

H₀: β₂ ≥ 0
H_a: β₂ < 0H₀: β₂ ≤ 0
H_a: β₂ > 0    H₀: β₂ = 0
H_a: β₂ ≠ 0H₀: β₂ = 0
H_a: β₂ > 0

Find the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

Question

Suppose a certain retailer sells several models of refrigerators. A random sample of the models sold by this retailer and their corresponding cubic feet (cu. ft.) and list price can be found below.

Model	Cu. Ft.	List Price
Model 1	18.3	$899.99
Model 2	24.8	$1,799.99
Model 3 with Thru-the-Door Ice and Water	25.4	$1,799.99
Model 4	19.3	$749.99
Model 5	17.3	$599.99
Model 6 with Thru-the-Door Ice and Water	19.6	$1,619.99
Model 7	25.0	$999.99
Model 8	24.5	$1,299.99
Model 9 with Thru-the-Door Ice and Water	25.4	$1,299.99
Model 10 with Thru-the-Door Ice and Water	26.0	$1,299.99
Model 11 with Thru-the-Door Ice and Water	25.6	$1,099.99
Model 12	18.0	$679.99
Model 13 with Thru-the-Door Ice and Water	25.0	$2,199.99
Model 14	20.8	$849.99
Model 15	15.5	$549.99
Model 16 with Thru-the-Door Ice and Water	28.2	$2,599.99
Model 17	27.8	$2,999.99
Model 18 with Thru-the-Door Ice and Water	26.6	$2,399.99
Model 19 with Thru-the-Door Ice and Water	22.6	$1,099.99
Model 20 with Thru-the-Door Ice and Water	21.8	$1,499.99
Model 21	20.9	$1,669.99

(a)

Develop the estimated simple linear regression equation to show how list price is related to the independent variable cubic feet. (Round your numerical values to four decimal places. Let

x₁

represent the cubic feet and y represent the list price.)

ŷ =

(b)

At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between list price and cubic feet.

State the null and alternative hypotheses.

H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₁ ≤ 0
H_a: β₁ > 0 H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ = 0
H_a: β₁ > 0

Find the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

State your conclusion.

Reject H₀. There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.Reject H₀. There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet. Do not reject H₀. There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.Do not reject H₀. There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet.

(c)

Develop a dummy variable that will account for whether the refrigerator has the thru-the-door ice and water feature. Code the dummy variable with a value of 1 if the refrigerator has the thru-the-door ice and water feature and with 0 otherwise. Use this dummy variable to develop the estimated multiple regression equation to show how list price is related to cubic feet and the thru-the-door ice and water feature. (Round your numerical values to four decimal places. Let

x₁

represent the cubic feet,

x₂

represent whether the refrigerator has the thru-the-door ice and water feature, and y represent the list price.)

ŷ =

(d)

At ? = 0.05, is the thru-the-door ice and water feature a significant factor in the list price of a refrigerator?

State the null and alternative hypotheses.

H₀: β₂ ≥ 0
H_a: β₂ < 0H₀: β₂ ≤ 0
H_a: β₂ > 0 H₀: β₂ = 0
H_a: β₂ ≠ 0H₀: β₂ = 0
H_a: β₂ > 0

Find the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

Accepted Answer

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