Question

X 28 39 32 37 44 22 40 Y 94 105 88 101 116 86 106 The coefficient of determination for the above bivariate data is: Question 12 options:

0.85

0.88

0.91

0.95

Answer 1

> x <- c(28, 39, 32, 37, 44, 22, 40)
> y <- c(94, 105, 88, 101, 116, 86, 106)
> model <- lm(y~x)
> summary(model)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5 6 7
3.0593 -0.1487 -8.1072 -1.5654 4.3932 2.8091 -0.4403

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 54.7750 8.6210 6.354 0.00143 **
x 1.2916 0.2443 5.287 0.00323 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.581 on 5 degrees of freedom
Multiple R-squared: 0.8483,   Adjusted R-squared: 0.8179
F-statistic: 27.96 on 1 and 5 DF, p-value: 0.003225

Hence, correct option is 0.85.