Question

Linear Regression and Correlation Activity Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age 16 - 19 20-24 25 - 34 35 - 54 55 - 74 75+ Number of Driver Death per 100,000 38 36 24 20 18 28 4. Can we use the regression line to make reliable prediction of the number of deaths per 100,000? (Is there a significant correlation between the two factors?) a. Find the p-value for a hypothesis test to if there is significant correlation. b. At the 5% significance level, what can you conclude about the correlation? C. Can we use the regression line to make reliable predictions?

Answer 1

(a) The p-value is 0.2288.

(b) The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

The p-value is 0.2288.

Since the p-value (0.2288) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the relationship is significant.

(c) Since the results are not significant, we cannot use the regression line to make reliable predictions.

	r²	0.335
	r	-0.579
	Std. Error	7.533
	n	6
	k	1
	Dep. Var.	Deaths
ANOVA table
Source	SS	df	MS	F	p-value
Regression	114.328	1	114.3276	2.01	.2288
Residual	227.006	4	56.7514
Total	341.333	5
Regression output					confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	35.582
Age	-0.192	0.1352	-1.419	.2288	-0.5671	0.1834