Question

In regression analysis, the total variation in the dependent variable, measured by the total sum of squares (SST), can be decomposed into two parts: the amount of variation that can be explained by the regression model, and the remaining unexplained variation.

True

False

In employing the randomised block design of ANOVA, the primary interest lies in reducing the within-treatments variation in order to make easier to detect differences between the treatment means.

True

False

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

True

False

When the error variable  is normally distributed and its standard deviation is a known constant, the test statistic for testing H 0 : β 1 = 0 in a simple linear regression follows the Student t-distribution with n – 1 degrees of freedom.

True

False

Answer 1

1)True

Since the total variation in the dependent variable=

the amount of variation that can be explained by the regression model/the remaining unexplained variation.

2)True

Since the blocks are homogeneous and as a result the within treatment variation becomes smaller.

3)True

Since rejection of the null hypothesis favours the alternative hypothesis and we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.  

4) False

Since when the error variable  is normally distributed and its standard deviation is a known constant, the test statistic for testing H 0 : β 1 = 0 in a simple linear regression follows the Student t-distribution with n – 2 degrees of freedom.