Question

Test the slope of the regression line for the following data. Use α=.01.

x 140 120 103 92 62 30 24

y 24 29 45 70 88 112 128

(Do not round the intermediate values. Round your answer to 2 decimal places.)

Observed t =

Fail to reject null hypothesis or reject null hypothesis

Answer 1

The statistical software output for this problem is :

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 144.42528 - 0.90188611 x
Sample size: 7
R (correlation coefficient) = -0.98684344
R-sq = 0.97385997
Estimate of error standard deviation: 7.1829277

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	144.42528	6.0353558	≠ 0	5	23.92987	<0.0001
Slope	-0.90188611	0.066080224	≠ 0	5	-13.648351	<0.0001

Observed t = -13.65

Critical value = 4.032

reject null hypothesis