Question

Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 12 15 The estimated regression equation is ? = 0.7 + 2.7x. Compute the mean square error using the following equation (to 3 decimals). Compute the standard error of the estimate using the following equation (to 3 decimals). Compute the estimated standard deviation b1 using the following equation (to 3 decimals). Use the t test to test the following hypotheses (? = .05): H0: B1 = 0 Ha: B1 /= 0. Compute the value of the t test statistic (to 2 decimals).

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: yi
Independent Variable: xi
yi = 0.7 + 2.7 xi
Sample size: 5
R (correlation coefficient) = 0.93831486
R-sq = 0.88043478
Estimate of error standard deviation: 1.8165902

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	0.7	1.9052559	? 0	3	0.36740472	0.7377
Slope	2.7	0.57445626	? 0	3	4.7000967	0.0182

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	72.9	72.9	22.090909	0.0182
Error	3	9.9	3.3
Total	4	82.8

Hence,

MSE = 3.3

Standard error = 1.817

Estimated standard deviation = 0.574

t test statistic = 4.70