Question

(2 points) For the data set (-2,-3), (0,2), (5,4), (8,7).(12, 10), carry out the hypothesis test HB: = 0 HB 70 Determine the value of the test statistic and the associated p-value. Test Statistic = p-Value = Note: In order to get credit for this problem all answers must be correct

Answer 1

Sol:

perform linear regression with lm fucntion in R

Rcode:

x <- c(-2,0,5,8,12)
y <- c(-3,2,4,7,10)
lmod <- lm(y~x)
summary(lmod)

Output:

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5
-1.4665 1.8567 -0.3354 0.1494 -0.2043

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 0.1433 0.8339 0.172 0.87451   
x 0.8384 0.1211 6.922 0.00618 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.387 on 3 degrees of freedom
Multiple R-squared: 0.9411,   Adjusted R-squared: 0.9214
F-statistic: 47.91 on 1 and 3 DF, p-value: 0.006181

ANSWER:

test statistic,t=6.922

p value=0.00618