Please Use R program do it. (a) Fit a simple linear regression model relating se

Question

Please Use R program do it.

(a) Fit a simple linear regression model relating selling price of the house to the current taxes ( x 1). Report your point estimates for all parameters of your model. Make a plot
of the data and the fitted regression line.

b. Test for significance of regression. which asks you to run and interpret an F test.
c. What percent of the total variability in selling price is explained by this model? asks you to interpret the sums-of-squares decomposition.

y x1 x2 x3 x4 x5 x6 x7 x8 x9 29.5 5.0208 1 3.531 1.5 2 7 4 62 0 27.9 4.5429 1 2.275 1.175 1 6 3 40 0 25.9 4.5573 1 4.05 1.232 1 6 3 54 0 29.9 5.0597 1 4.455 1.121 1 6 3 42 0 29.9 3.891 1 4.455 0.988 1 6 3 56 0 30.9 5.898 1 5.85 1.24 1 7 3 51 1 28.9 5.6039 1 9.52 1.501 0 6 3 32 0 35.9 5.8282 1 6.435 1.225 2 6 3 32 0 31.5 5.3003 1 4.9883 1.552 1 6 3 30 0 31 6.2712 1 5.52 0.975 1 5 2 30 0 30.9 5.9592 1 6.666 1.121 2 6 3 32 0 30 5.05 1 5 1.02 0 5 2 46 1 36.9 8.2464 1.5 5.15 1.664 2 8 4 50 0 41.9 6.6969 1.5 6.902 1.488 1.5 7 3 22 1 40.5 7.7841 1.5 7.102 1.376 1 6 3 17 0 43.9 9.0384 1 7.8 1.5 1.5 7 3 23 0 37.5 5.9894 1 5.52 1.256 2 6 3 40 1 37.9 7.5422 1.5 5 1.69 1 6 3 22 0 44.5 8.7951 1.5 9.89 1.82 2 8 4 50 1 37.9 6.0831 1.5 6.7265 1.652 1 6 3 44 0 38.9 8.3607 1.5 9.15 1.777 2 8 4 48 1 36.9 8.14 1 8 1.504 2 7 3 3 0 45.8 9.1416 1.5 7.3262 1.831 1.5 8 4 31 0 25.9 4.9176 1 3.472 0.998 1 7 4 42 0

Explanation / Answer

Sol:

code:

mod1 <- lm(sphouse$y~sphouse$x1,data=sphouse)

output:

Call:

lm(formula = sphouse$y ~ sphouse$x1, data = sphouse)

Residuals:

Min 1Q Median 3Q Max

-3.8343 -2.3157 -0.3669 1.9787 6.3168

Coefficients:

Estimate Std. Error t value

(Intercept) 13.3202 2.5717 5.179

sphouse$x1 3.3244 0.3903 8.518

Pr(>|t|)

(Intercept) 3.42e-05 ***

sphouse$x1 2.05e-08 ***

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Signif. codes:

0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.961 on 22 degrees of freedom

Multiple R-squared: 0.7673, Adjusted R-squared: 0.7568

F-statistic: 72.56 on 1 and 22 DF, p-value: 2.051e-08

regression eq is

y=13.32+3.32x1

slope=3.32

y intercept=13.32

slope=3.32

y intercept=13.32

Intrepretation of y intercept

when x1=0

price=13.32

selling price is 13.32 when there are no taxes

intrepretaion of slope

slope=3.32

change in y/change in x=3.32

For unit increase in current tax, price increases by 3.32

Solutionb:

F-statistic: 72.56 on 1 and 22 DF, p-value: 2.051e-08

p<0.05

model is significant

Solutionc:

Multiple R-squared: 0.7673,

76.73% variation in y is explained by model.good model.

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