Question

The following regression output is available. Notice that some of the values are missing.

Regression Statistics

Multiple R	0.754525991
Adjusted R Square	0.507782253
Standard Error

  ANOVA

	df	SS	MS
Regression	1
Residual	7	27.3727758	3.910397
Total	8	63.55555556

	Coefficients	Standard Error
Intercept	4.822953737	2.20457789
X	0.053825623	0.017694916

Pt 1. Given this information, what is the standard error of the estimate for the regression model?

Pt 2.  Given this information, what was the sample size used in the study?

Pt 3. Given this information, what percent of the variation in the y variable is explained by the independent variable?

Pt 4. Given this information, what is the test statistic for testing whether the regression slope coefficient is equal to zero?

Answer 1

Answer 1:

The formula standard error of the estimate for the regression model is as follows:

Here, Σ(Y-Y')² = Sum of Squared Errors = 27.3727758 and N - 1 = 8. Thus, N = 8 + 1 = 9 (Refer to ANOVA table)

Standard error of the estimate for the regression model = SQRT(27.3727758/9)

Standard error of the estimate for the regression model = 1.7440

Answer 2:

From ANOVA table, it can be seen that

n - 1 = 8

Thus, n = 8 + 1 = 9

The sample size used in the study is 9

Answer 3:

R-squared value indicates percentage of variance in dependent variables that is explained by independent variables.

In this case, R value is 0.754525991. so R-square value = 0.754525991*0.754525991 = 0.569309471

This means that 56.9309471% variation in the y variable is explained by the independent variable