Question

The county assessor is interested in developing a model to estimate the market value of residential property and the assessor feels that the most important variable that selling price depends on is the size of the house.

1)As you observe the scatter plot on the next slide is the relationship between selling price and size positive or negative? Also explain why you give the answer you give.

2)What is the estimated regression equation for selling price depending on the size of the property (please round the ?

3)What do you conclude about the slope null hypothesis that β= 0, and the alternative that β is not equal to zero. Also tell me what number(s) you use from the Excel to make this conclusion.

4)What is the value of R square and what does this number mean?

Selling Price Size ( 100's sr ft) (1000's) Selling Price (1000's) 12 20.2 27 30 30 21.4 21.6 25.2 37.2 14.4 15 22.4 23.9 26.6 30.7 265.2 279.6 311.2 328 352 281.2 288.4 292.8 356 263.2 272.4 291.2 299.6 307.6 320.4 400 350 300 250 200 150 100 50 0 10 25 35 sSize (1o0's sqr ft) 40 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.940607241 0.884741981 0.87587598 10.13202785 15 ANOVA df MS Significance F Regression Residual Total 1 13 14 10244.28349 10244.28349 99.79041726 1334.553848 102.6579883 11578.83733 1.82|27Е-07 P-value Coefficients Standard Error t Stat 206.2789776 9.79643104 21.05654363 1.98187E-11 185.1150751 227.4428802 3.955859439 0.396001137 9.989515366 1.82127E-07 3.100350996 4.811367883 Lower 95% Upper 95% Intercept Size (sqr ft)

Answer 1

1) The relationship between price and size is positive as it can be seen from the scatter plot that as the size of property increases the selling price also increases.

2) Equation can be observed from coefficients  of intercept and size from the table

Regression equation is in the form :Y= a + βX

where a = intercept

β =slope of X

X = size(. sq.ft)

Y = 206.2789 + 3.9556X

3)H_o : null hypothesis β= 0

Ha = alternate hypotheses = β not equal to 0

since number of observations are small , we use t test here

t = {estimated slope value of   β - populated value( i.e = 0 )}/standard error of size( sqr.ft )

= 3.9556 - 0 / 0.3960

=9.9889

assuming a significance level of 5% , t value from table = 1.96

since calculated t value > critical value from table

9.9889> 1.96

so we reject the null hypothesis that  β = 0

4 )R² = 88.47%

this means that 88.47% of the variation in selling price of house are explained by house size(sqr.ft)