A Realtor examines the factors that influence the price of a house in Arlington,

Question

A Realtor examines the factors that influence the price of a house in Arlington, Massachusetts. He collects data on recent house sales (Price) and notes each house’s square footage (Sqft) as well as its number of bedrooms (Beds) and number of bathrooms (Baths). A portion of the data is shown in the accompanying table. Use Table 2 and Table 4. Price Sqft Beds Baths Price Sqft Beds Baths 840,000 2,768 4 3.5 495,000 1,692 3 2.0 822,000 2,500 4 2.5 463,000 1,714 3 2.0 713,000 2,400 3 3.0 457,000 1,650 3 2.0 689,000 2,200 3 2.5 451,000 1,685 3 2.0 685,000 2,716 3 3.5 435,000 1,500 3 1.5 645,000 2,524 3 2.0 431,700 1,896 2 1.5 625,000 2,732 4 2.5 414,000 1,182 2 1.5 620,000 2,436 4 3.5 401,500 1,152 3 1.0 587,500 2,100 3 1.5 399,000 1,383 4 1.0 585,000 1,947 3 1.5 380,000 1,344 4 2.0 583,000 2,224 3 2.5 380,000 1,272 3 1.0 569,000 3,262 4 2.0 375,900 2,275 5 1.0 546,000 1,792 3 2.0 372,000 1,005 2 1.0 540,000 1,488 3 1.5 367,500 1,272 3 1.0 537,000 2,907 3 2.5 356,500 1,431 2 2.0 516,000 1,951 4 2.0 330,000 1,362 3 1.0 511,000 1,752 3 1.5 330,000 1,465 3 1.0 510,000 1,727 3 2.0 307,500 850 1 1.0 PictureClick here for the Excel Data File a. Estimate: Price = 0 + 1 Sqft + 2 Beds + 3 Baths + . (Round your answers to 2 decimal places.) 1111formula277.mml = + Sqft + Beds + Baths b-1. Choose the appropriate hypotheses to test whether the explanatory variables are jointly significant in explaining price. H0: 1 = 2 = 3 = 0; HA: At least one j > 0 H0: 1 = 2 = 3 = 0; HA: At least one j 0 H0: 1 = 2 = 3 = 0; HA: At least one j < 0 b-2. Find the value of the appropriate test statistic. (Round your answer to 4 decimal places.) Test statistic b-3. At the 5% significance level, what is the conclusion to the test? Are the explanatory variables jointly significant in explaining Price? Reject H0; the explanatory variables are jointly significant in explaining Price. Reject H0; the explanatory variables are not jointly significant in explaining Price. Do not reject H0; the explanatory variables are jointly significant in explaining Price. Do not reject H0; the explanatory variables are not jointly significant in explaining Price. c-1. Choose the appropriate hypotheses to test whether each of the explanatory variables are individually significant in explaining Price. H0: j = 0; HA: j > 0 H0: j = 0; HA: j < 0 H0: j = 0; HA: j 0 c-2. At the 5% significance level, are all explanatory variables individually significant in explaining Price? Explanatory Variables Significant in Explaining Price Sqft Beds Baths rev: 11_12_2015_QC_CS-31836, 10_13_2016_QC_CS-65617

Explanation / Answer

Using minitab:

Regression Analysis: Price versus Sq. Ft., Beds, Baths

Analysis of Variance

Source         DF       Adj SS       Adj MS F-Value P-Value
Regression      3 4.71211E+11 1.57070E+11    27.93    0.000
Sq. Ft.       1 41227441014 41227441014     7.33    0.011
Beds          1      4239740      4239740     0.00    0.978
Baths         1 76108538920 76108538920    13.54    0.001
Error          32 1.79928E+11   5622747851
Lack-of-Fit 31 1.79850E+11   5801606653    74.26    0.092
Pure Error    1     78125000     78125000
Total          35 6.51138E+11

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
74985.0 72.37%     69.78%      62.46%

Coefficients

Term        Coef SE Coef T-Value P-Value   VIF
Constant 153348    57142     2.68    0.011
Sq. Ft.     95.9     35.4     2.71    0.011 2.73
Beds         557    20280     0.03    0.978 1.43
Baths      92023    25012     3.68    0.001 2.13

Regression Equation

Price = 153348 + 95.9 Sq. Ft. + 557 Beds + 92023 Baths

Use the p-values to determine which coefficients in the model are significantly different from zero (no effect).

The coefficients table lists the estimated coefficients for each level of each categorical factor. Before you look at the effects for specific levels in the coefficients table, you should look first in the analysis of variance table at the p-value for each term. After you identify a significant set of effects (for example main effects, or interaction effects), use the coefficients table to evaluate the individual effects.

If the analysis of variance table suggests significant higher-order or interaction effects, you should look at them first because they will influence how you interpret the main effects. To use the p-value, you need to:

·    Identify the p-value for the effect you want to evaluate.

·    Compare this p-value to your a-level . A commonly used a-level is 0.05.

-    if the p-value is less than or equal to a, conclude that the effect is significant.

-    if the p-value is greater than a, conclude that the effect is not significant.

Here

For given data, the results can be summarized as follows:

·    Sq.Ft is a significant coefficient (P = 0.011) and does have a significant interaction with any other predictor.

·    Beds is not significant coefficient (P = 0.978).

·    Baths is not significant coefficient (P = 0.001).

Hope this will be helpful. Thanks :)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.