Question

X 40 30 26 46 36 28 20

Y 154 130 84 147 158 98 71

The intercept of the OLS regression line for the above bivariate data is:

Question 7 options:

-6.65

-3.52

3.52

6.65

X	29	24	40	22	43	36	33
Y	46	51	42	52	41	46	46

The standard error of the estimate for the above bivariate data is:

Question 11 options:

	1.08
	1.18
	1.28
	1.38

Answer 1

I used R software to solve this question.

R codes and output:

> X=c(40,30, 26, 46, 36, 28, 20)
> Y=c(154, 130, 84, 147, 158, 98, 71)
> fit=lm(Y~X)
> fit

Call:
lm(formula = Y ~ X)

Coefficients:
(Intercept) X
6.645 3.520

>
> X=c(29,24,40,22,43,36,33)
> Y=c(46,51,42,52,41,46,46)
> fit=lm(Y~X)
> summary(fit)

Call:
lm(formula = Y ~ X)

Residuals:
1 2 3 4 5 6 7
-2.009174 0.477446 -0.479740 0.472095 0.028287 1.509557 0.001529

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 62.58677 2.03419 30.767 6.81e-07 ***
X -0.50268 0.06119 -8.214 0.000435 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.183 on 5 degrees of freedom
Multiple R-squared: 0.931, Adjusted R-squared: 0.9172
F-statistic: 67.48 on 1 and 5 DF, p-value: 0.0004353

Que.7

Intercept = 6.65

Que.11

Standard error = 1.18