Question

Psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded.

Hours without sleep	32	38	48	24	46	35	30	34	42
Number of Mistakes	6	8	13	5	7	6	5	8	12

Hours without sleep=x, Number of mistakes=y

(a) Find the equation of regression line. Round slope and y-intercept to nearest thousandth.  

(b) Find the residual when the number of hours is 32 hours.  Analyze the result.  

(c) Apply critical value test (not hypothesis testing).  Show inequality. By using critical value test, is there linear relation exists?  

Answer 1

(a) The equation of regression line is:

y = -2.7677 + 0.2885*x

(b) y = -2.7677 + 0.2885*32 = 6.464

Residual = 6 - 6.464 = -0.464

(c) The hypothesis being tested is:

H₀: $\rho$ = 0

H_a: $\rho$ ≠ 0

t = 3.2

The critical value is 2.36.

Since 3.2 > 2.36, we can reject the null hypothesis.

Therefore, we can conclude that there is a linear relation.

	r²	0.594
	r	0.771
	Std. Error	1.979
	n	9
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	40.1307	1	40.1307	10.24	.0151
Residual	27.4249	7	3.9178
Total	67.5556	8
Regression output				confidence interval
variables	coefficients	std. error	t (df=7)	p-value	95% lower	95% upper
Intercept	-2.7677
x	0.2885	0.0901	3.200	.0151	0.0753	0.5016