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 Ha: β1 < 0H0: β1 ≤ 0 Ha: β1 > 0 H0: β1 = 0 Ha: β1 ≠ 0H0: β1 = 0 Ha: 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 Ha: β2 < 0H0: β2 ≤ 0 Ha: β2 > 0 H0: β2 = 0 Ha: β2 ≠ 0H0: β2 = 0 Ha: β2 > 0 Find the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.)

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 Ha: β1 < 0H0: β1 ≤ 0 Ha: β1 > 0 H0: β1 = 0 Ha: β1 ≠ 0H0: β1 = 0 Ha: 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 Ha: β2 < 0H0: β2 ≤ 0 Ha: β2 > 0 H0: β2 = 0 Ha: β2 ≠ 0H0: β2 = 0 Ha: β2 > 0 Find the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.)

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