Dfsfdzvdfv

The random errors, ’s (epsilons), are assumed to be independently and normally distributed with mean equal to zero and a constant (but unknown) variance 2.

SOURCE | DF | SS | MS | F | P |

Regression | 1 | SSR | MSR = SSR | MSR/MSE | p-valu |

Error | n – 2 | SSE | MSE = SSE/( n – 2) | | |

Total | n – 1 | SST | | | |

1 Test the usefulness of the model

Reject H0 if |t| > tn-2, /2 and do not reject otherwise (for two-tailed test).

You can also construct a confidence interval for 1 and the formula is: .

If the confidence interval doesn’t cover 0, the null hypothesis can be rejected at

r2 = R2 in a simple regression model. ;

2 Make Prediction the mean of y when x = xp for y when x = xp

R2 (Coefficient of Multiple Determination) and adjusted R2 both measure the total percentage of variations of Y around the mean of Y that can be explained by the regression equation. Hence, the higher the value of R2, the better the model fits the data. As more independent variables are added to the model, R2 always increases and SSE always decreases. This fact that R2 = 1 – SSE/SST implies that R2 and SSE always go in the opposite direction., we sometimes use “adjusted R2” to measure the fitness of the model when the sample size relative to the number of independent variables is small.

;

. Thus, as n ∞ (keeping k constant), .

Global f test can be used to test the overall usefulness of the model.

H0: 1 = 2 = … k = 0 H1: At least one of the i’s 0

Test Statistic: F = MSR/MSE. Decision Rule: Reject H0 if F > Fk, n-k-1, .

To determine whether the complete model has better predictive power than the reduced model, we can do partial F test. This test allows us to determine whether the additional terms in the full model are really necessary.

H0: g+1 = g+2 = … = k = 0

H1: At least one of the parameters being tested is nonzero.

The standard error of the sample mean = The population standard deviation...