Question

In: Statistics and Probability

Write the equation of the line. What is r? What is r squared? Using the equation...

Write the equation of the line.
What is r?
What is r squared?
Using the equation of the line if x is 25 what is y?
Using the equation of the line if y is 20 what is x.
x 25 32 27 24 26 18 20 23 20 16 19 15 20 27 27
y 28 34 36 28 31 22 24 26 24 23 22 13 23 35 29

Solutions

Expert Solution

I used R software to solve this question.

R codes and output:

> x=c(25,32,27,24,26,18,20,23,20,16,19,15,20,27,27)
> y=c(28,34,36,28,31,22,24,26,24,23,22,13,23,35,29)
> fit=lm(y~x)
> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-4.8794 -1.1275 -0.1275 0.6499 4.4565

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7991 3.4361 0.233 0.82
x 1.1387 0.1489 7.645 3.66e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.671 on 13 degrees of freedom
Multiple R-squared: 0.818, Adjusted R-squared: 0.804
F-statistic: 58.45 on 1 and 13 DF, p-value: 3.662e-06

1.

The equation of the line is

Y = 0.7991 + 1.1387 X

2.

r =

3.

r2 = 0.818

4.

If x is 25 then

Y = 0.7991 + 1.1387 X

Y = 0.7991 + 1.1387 (25)

Y = 29.2666

5.

If y is 20 then

Y = 0.7991 + 1.1387 X

20 = 0.7991 + 1.1387 X

X = (20 - 0.7991) / 1.1387

X = 16.8621

orchestra answered 2 years ago
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