Question

In: Statistics and Probability

What is the coefficient of determinaton and cofficient of correlation for this data set home prices...

What is the coefficient of determinaton and cofficient of correlation for this data set

home prices vs square footage.

369,000 1,372
569,000 2909
439000 1837
544000 2573
399000 1642
499000 2216
599000 1400
487000 2508
410000 1800
379950 1674
565000 2056
659000 4171
859000 4308
610000 2303
450000 1698
480000 1896
319900 1970
385000 2320
449000 2846
199000 1440
369000 2295
350000 1512
449000 1900
525000 2080
770000 3168
789000 3236
675000 2784
765000 2802

Solutions

Expert Solution

Import the data set into R and store it into a data frame named dat.

Home_Price Sq_ft
369,000 1,372
569,000 2909
439000 1837
544000 2573
399000 1642
499000 2216
599000 1400
487000 2508
410000 1800
379950 1674
565000 2056
659000 4171
859000 4308
610000 2303
450000 1698
480000 1896
319900 1970
385000 2320
449000 2846
199000 1440
369000 2295
350000 1512
449000 1900
525000 2080
770000 3168
789000 3236
675000 2784
765000 2802

R Code Output-

> cor(dat$Home_Price,dat$Sq_ft)

[1] 0.7610977

> summary(lm(dat$Home_Price~dat$Sq_ft))

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 146970.69 64293.42 2.286 0.0307 *  

dat$Sq_ft 158.35 26.47 5.983 2.57e-06 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 104700 on 26 degrees of freedom

Multiple R-squared: 0.5793, Adjusted R-squared: 0.5631

F-statistic: 35.8 on 1 and 26 DF, p-value: 2.572e-06

Hence ,the correlation coefficient =0.7610977 and the coefficient of determination= 0.5793.


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