Test the significance of the slope. What is your t-value for the slope? Do you c

Question

Test the significance of the slope. What is your t-value for the slope? Do you conclude that there is no significant relationship between the two variables or do you conclude that there is a significant relationship between the variables? $379,900 $399,900 $419,900 $419,900 $420,000 $449,000 $449,900 $459,900 $479,900 $499,000 $499,999 $528,900 $544,500 $549,000 $549,000 $569,000 $569,900 $575,000 $599,000 $629,900 $634,900 $649,000 $675,000 $689,000 $699,900 $729,000 $729,900 $738,000 $759,900 $775,000 $789,900 $799,000 $799,000 $823,000 $829,000 $849,000 $859,000 $863,000 $869,000 $875,000 $875,000 $899,000 $929,900 $949,000 $969,900 $979,000 $995,000 $999,000 $1,050,000 $1,075,000 $1,075,000 $1,089,000 $1,175,000 $1,199,000 $1,199,000 $1,199,000 $1,199,000 $1,199,000 $1,199,500 $1,199,900 $1,200,000 $1,225,000 $1,250,000 $1,250,000 $1,250,000 $1,269,000 $1,275,000 $1,280,000 $1,295,000 $1,300,000 $1,325,000 $1,340,000 $1,345,000 $1,349,000 $1,349,000 $1,350,000 $1,389,000 $1,398,880 $1,399,000 $1,399,000 $1,419,000 $1,449,000 $1,459,000 $1,475,000 $1,495,000 $1,499,000 $1,500,000 $1,500,000 $1,535,000 $1,649,000 $1,650,000 $1,689,000 $1,695,000 $1,699,000 $1,739,000 $1,749,000 $1,759,000 $1,779,000 $1,795,000 $1,799,000 2,495 2,543 2,584 2,593 2,600 2,700 2,704 2,709 2,735 2,754 2,900 2,912 2,996 3,006 3,097 3,116 3,140 3,149 3,156 3,196 3,200 3,209 3,225 3,268 3,269 3,280 3,316 3,366 3,388 3,410 3,446 3,500 3,519 3,522 3,568 3,5 1,160 1,161 1,265 1,274 1,440 1,451 1,468 1,472 1,486 1,547 1,618 1,823 1,857 1,923 1,924 1,975 2,002 2,047 2,060 2,060 2,136 2,300 2,318 2,364 2,365 2,418 2,422 In this example, the independent variable (x) is defined as the square footage, and the dependent variable (y) is defined as the listing prices. The square footage of a home provides a basis for predicting the listing price. However; in no event does a home begin with a listing price and then has a square footage set for it

Explanation / Answer

Here independent variable x = square footage

and dependent variable y = listing price

Here we have to test the hypothesis that,

H0 : B = 0 Vs H1 : B not = 0

Where B is population slope for x.

Assume alpha = 5% = 0.05

This we can done using MINITAB.

steps :

Stat --> regression --> regression --> Response : y --> predictors : x --> Results : select second option --> ok --> ok

Output is :

Regression Analysis: y versus x

The regression equation is
y = 1190170 - 156 x

Predictor Coef SE Coef T P
Constant 1190170 100404 11.85 0.000
x -155.63 38.49 -4.04 0.000

S = 236340 R-Sq = 21.1% R-Sq(adj) = 19.8%

Analysis of Variance

Source DF SS MS F P
Regression 1 9.13177E+11 9.13177E+11 16.35 0.000
Residual Error 61 3.40725E+12 55856618714
Total 62 4.32043E+12

The test statistic t = -4.04 and P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Population slope is differ than 0.

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