Example: We want to study the relationship between home price and house size and

Question

Example: We want to study the relationship between home price and house size and its location in one of two subdivisions.. Two subdivisions are, Oak Knoll and Hidden Hills. Y -selling price (thousand dollars) Xi-house size (saft) X2 = 1 if house in Oak Knoll 0 if house in Hidden Hills We assume that the true relationship could be expressed as price = ?? + A(size) + ?2(location) + ? Where, price is in (S000) and location1 if in Oak Knoll and 0 if in Hidden Hills. Using a small sample of 20 homes, the study produced the following output SUMMARY OUTPUT ression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.960379757 0.922329279 0.913191547 29.66970508 20 ANOVA df MS Regression Residual Total 2 177706.7957 88853.4 100.9363 7 14964.95379 880.2914 19 192671.7495 0.0000 Coefficients Standard Error t Stat Intercept SqFt Oak Knol P-value Lower 95% Upper 95% ower 95 0loper 95 09 83.8431 105.0802 -83.8431 105.0802 0.1688 0.2286 0.1688 0.2286 3.2987 63.7779 3.2987 63.7779 10.6185 0.1987 44.7725 0.2372 0.8154 0.0142 14.0076 0.0000 14.3328 2.3400 0.0317 Based on this output, answer the following 1. Find the best estimates of Po. B1 and ßz 2. Ata -0.05, is there sufficient evidence to indicate that the larger the size of the house the higher the price? 3. Find the p-value for determining whether the above model is useful in explaining home price 4. Find the estimated coefficient in the relationship between price and size 5. What is the value of test statistic for testing whether there is a relationship between price and location. 6. Find the proportion of the variation in home price in our sample which can be

Explanation / Answer

Please see below the answers: -

1)

B0= 10.6185

B1= 0.1987

B2= 33.5383

2)

Looking at the p-value for SqFt, we can conclude that larger the size of the house, higher the price

3)

P-value is Significance F which is 0.00

4)

r is 0.96 which means that there is a positive relationship between the two variables

5)

B2= 33.5383

6)

r^2 is 0.9223 which means 92.23% of the variation in dependent variable is accounted for by the independent variables.

7)

0.00

8)

33.5383

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