Question

The following data are measurements of tensile strength in MPa (megapascals) and hardness (Rockwell E scale, dimensionless) for 20 pieces of die-cast aluminium. A least-squares regression line has been fitted and displayed on a scatterplot of the data.

Sample	Strength	Hardness	Sample	Strength	Hardness
1	202	53	11	205	60
2	241	70	12	201	51
3	234	78	13	262	95
4	234	55	14	238	88
5	234	64	15	177	51
6	244	71	16	183	54
7	222	82	17	170	52
8	230	67	18	197	64
9	170	56	19	223	83
10	240	86	20	194	56

Click here to download the MATLAB data file

What can be concluded from the P-value in the Analysis of Variance Table, using significance level 0.01?

Answer 1

Output using excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.767040848
R Square	0.588351663
Adjusted R Square	0.565482311
Standard Error	17.92457485
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	8265.7231	8265.723094	25.72664329	7.94408E-05
Residual	18	5783.226906	321.2903837
Total	19	14048.95
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	116.1018794	19.91562859	5.829686914	1.60035E-05	74.26069633	157.9430624
X	1.481259291	0.292038107	5.072143856	7.94408E-05	0.867709995	2.094808587

p-value = 0.0001

As p-value = 0.0001 < 0.01, we reject the null hypothesis.

There is a relationship between variables