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

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.

orchestra answered 3 years ago

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