Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 12

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).

Explanation / Answer

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:

Analysis of variance table for regression model:

Hence,

MSE = 3.3

Standard error = 1.817

Estimated standard deviation = 0.574

t test statistic = 4.70

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

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