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?
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)Ho : 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)
The county assessor is interested in developing a model to estimate the market value of residential...
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