The questions involve the data set for asking prices of Richmond townhouses obta

Question

The questions involve the data set for asking prices of Richmond townhouses obtained on 2014.11.03 For your subset, the response variable is asking price divided by 10000 askpr-c(58.39, 65.99, 86.8, 55.8, 25.9, 57.8, 47.8, 40.8, 26.99, 51.68, 71.99, 44.8, 58.8, 33.7, 51.99, 79.99, 61.5, 68.5, 62.8888, 78.8, 50.8, 50.5, 81.9, 68.8, 79.8, 41.99, 53.8, 68.8, 60.8, 40.9, 108.8, 53.8, 40.8, 47.9, 53.9, 52.4, 56.88, 59.8, 74.8, 49.9) The explanatory variables are (i) finished floor area divided by 100 farea-c(15.09, 22.78, 15.08, 13.06, 6.1, 13.84, 13.34, 14, 10.5, 15.1, 15.05, 9.4, 17.37, 12, 12.09, 22, 14.5, 15.76, 15.77, 19.48, 16.6, 12.26, 20.95, 15.95, 15.25, 12.9, 10.95, 16.9, 13.2, 16.06, 23.98, 12.22, 12.26, 12.1, 11.84, 16.22, 15.78, 17.63, 17.48, 15.6) (ii) age age-c(8, 35, 1, 0, 11, 10, 32, 38, 37, 20, 8, 14, 26, 28, 7, 20, 7, 4, 6, 11, 23, 3, 19, 18, 3, 44, 18, 8, 3, 25, 16, 9, 29, 7,15, 25, 17, 26, 5, 20) You are to fit a multiple regression model with the response variable askpr and two explanatory variables farea, age richmondtownh-data.frame(askpr,ffarea,age) After fitting the regression model, get the vector of fitted or predicted values ý Please use 3 significant digits for the answers below which are not integer-valued Part a) The values of R2 for the regression model with 2 explanatory variables is: 2 explanatory: Part b) Let yi be the values of askpr and let ý, be the fitted values fori -1,...,n - 40 The sample mean of the yi IS and the sample SD of the yi is The sample mean of the ý, is and the sample SD of the ý, is

Explanation / Answer

Part a)

R-squared: 0.8156

Part b)

yi = askpr and yi^ is it's predicted value :

Part c : Covariance between Yi and Yi^

Cov (Yi , Yi^) = 224.7405

Correlation between Yi and Yi^ is

Corr(Yi , Yi^) = 0.9030794

Part d) : Correlation of Yi and Yi^ (0.903079) and R^2 (0.8156) are not match

Part e) : The correlation between Yi and Wi is 0.897518

Part f) : Yes , the correlation in C is large

R Code for your referance :

Yi = askpr

Yi^ = pred

askpr=c(58.39, 65.99, 86.8, 55.8, 25.9, 57.8, 47.8, 40.8, 26.99, 51.68, 71.99, 44.8, 58.8, 33.7, 51.99, 79.99, 61.5, 68.5, 62.8888, 78.8, 50.8, 50.5, 81.9, 68.8, 79.8, 41.99, 53.8, 68.8, 60.8, 40.9, 108.8, 53.8, 40.8, 47.9, 53.9, 52.4, 56.88, 59.8, 74.8, 49.9)
ffarea=c(15.09, 22.78, 15.08, 13.06, 6.1, 13.84, 13.34, 14, 10.5, 15.1, 15.05, 9.4, 17.37, 12, 12.09, 22, 14.5, 15.76, 15.77, 19.48, 16.6, 12.26, 20.95, 15.95, 15.25, 12.9, 10.95, 16.9, 13.2, 16.06, 23.98, 12.22, 12.26, 12.1, 11.84, 16.22, 15.78, 17.63, 17.48, 15.6)
age=c(8, 35, 1, 0, 11, 10, 32, 38, 37, 20, 8, 14, 26, 28, 7, 20, 7, 4, 6, 11, 23, 3, 19, 18, 3, 44, 18, 8, 3, 25, 16, 9, 29, 7, 15, 25, 17, 26, 5, 20)
model = lm(askpr~ffarea+age)
aov(model)
summary(model)
pred = 14.1104+3.7329*ffarea-0.7170*age
mean(pred)
sqrt(var(pred))
mean(askpr)
sqrt(var(askpr))
cov(askpr,pred)
cor(askpr,pred)

wi = 15.8943+3.83288*ffarea-0.916983*age
cor(wi,askpr)

>>>>>>>>>>> Best Luck >>>>>>>>>>>

Estimate Yi Yi^ Mean 58.19947 16.60017 Standered Deviation 58.19522 14.99142

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