7.2: Goodness of Fit and Hypothesis Tests Flashcards
Sum of Squares Regression (SSR) formula:
SSR = Σ(Y^ - ȳ)^2
Sum of Squared Totals (SST) formula:
SST = Σ(Yi - ȳ)^2
Sum of Squared Errors (SSE) formula:
SSE = Σ(Yi - ȳ)^2
SSE = Σ(Yi - ȳ)^2
Measures to evaluate goodness of fit of SLR:
1 - The coefficient of determination,
2 - The F-statistic for the test of fit,
3 - Standard error of the regression.
Coefficient of determination is the percentage of…
variation of the dependent variable that is explained by the independent variables.
*Also referred to as the R-squared or R2.
Coefficient of determination formula:
Coeff.of.Determination = Σ(Y^i - ȳ)^2 / Σ(Yi - ȳ)^2
Mean Square Regression (MSR) is the sum of…
Squares regression divided by the number of independent variables k; in a simple linear regression, k = 1.
Formula of for Mean Square Regression (MSR) in simple linear regression:
MSR = Σ(Yi - ȳ)^2
Mean Square Error (MSE) is the sum of…
Squares error divided by the degrees of freedom: n − k − 1;
In a simple linear regression, n − k − 1 = n − 2.
Mean Square Error (MSE) formula:
MSE = Σ(Yi - ȳ)^2 / n-k-1
The F-distributed test statistic (MSR/MSE) formula is:
F = MSR/MSE
Analysis of Variance (ANOVA) is the analysis that…
Breaks the total variability of a dataset (such as observations on the dependent variable in a regression) into components representing different sources of variation.
Standard error of the estimate is a measure of the fit of…
A regression line, calculated as the square root of the mean square error.
*Also known as the standard error of the regression and the root mean square error.
Standard error of the estimate formula:
(se) = √MSE = √ Σ(Yi - ȳ)^2 / n-2
