Lot Size Regression Problem Nov 20 SOLVED
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New York University *
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103
Subject
Statistics
Date
Jan 9, 2024
Type
docx
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2
Uploaded by BailiffNewtMaster1012
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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