Lot Size Regression Problem Nov 20 SOLVED

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New York University *

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103

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Statistics

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Jan 9, 2024

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Regression Equation Price ($T) = 182.8 + 17.89 Lot Size (000 sq ft) Coefficients Term Coef SE Coef T- Value P- Value VIF Constant 182.8 22.0 8.29 0.000   Lot Size (000 sq ft) 17.89 2.60 6.87 0.000 1.00 Model Summary S R-sq R- sq(adj) R- sq(pred) 102.95 6 24.18% 23.67% 21.34% Analysis of Variance Source DF Adj SS Adj MS F- Value P- Value Regression 1 500295 500295 47.20 0.000 Error 148 156877 7 10600     Total 149 206907 1       1. Is there evidence of a linear relationship between Price and Lot Size? Use alpha =.01. Alpha = .01 H0: Beta1 =0 HA: Beta1 neq 0 Test stat: t = b1/sb1 Tc is 6.87 and p-val = 0 < .01. 2. Construct a 90% CI for Beta1 and interpret it. 17.89 +/- 1.645 * 2.60 3. Provide the value and an interpretation of s_e. S_e is given as 102.956. We expect approx. 95% of the observations to lie within 2s_e of the estimated regression line. 4. What proportion of variability in y is explained by the regression? The R^2 is 24.18% or .2418. 5. What is the value of s_x? SS_xx = (s_e)^2 / (sb_1)^2 which implies that S^2x is SS_xx/(n-1) and s_x is sqrt(S^2_x) S_x is approx. 3.244
6. If you wanted to predict the price of a home on 8000 sq feet (Lot size =8), would you use a CI for E(y|x) or a PI for y|x? PI since we are looking for the price of an actual house on 8000 sq feet of lot size not the average price for houses on 8000 sq feet of lot size.
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