Question

# Given are five observations for two variables, x and y. xi 1 2 3 4 5...

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).

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