Question

6.    The analysis of variance methodology will show that there really is a difference between the means of several groups when:   

a.    the variance within groups is significantly larger than the variance between groups.

b.    the variance between groups is significantly larger than the variance within groups.

            c.         the sum of squares within groups is large relative to the sum of squares total.

d.    the sample means across the treatment groups are identical and equal the grand mean.

            e.         none of the above.

7.    If all of the data points for a simple regression were on the regression line then the coefficient of determination would equal:

            a.         -1

            b.         0

            c.         1

            d.         n, where n is the sample size.

            e.         k, where k is the number of independent variables.

8.    In regression analysis, the width of the prediction interval estimate for the individual value of Y is dependent on

            a.         the standard error of the estimate.

            b.         the value of X for which the prediction is being made.

            c.         the size of the sample.

            d.         all of the above.

            e.         both (a) and (c).

9.    The estimated regression line is defined as the straight line that:

            a.         touches the most points in the scatter diagram.

            b.         maximizes the SSE or the sum of squared errors.

c.    minimizes the sum of the absolute deviations between the line and the corresponding observations.

d.    minimizes the sum of the squared vertical distances between each observation and the line.

e.    none of the above

Answer 1

Answer 6. b. the variance between groups is significantly larger than the variance within groups.

Explanation:

For ANOVA, we have the Null Hypothesis, Ho: There is no significant difference between means of several groups and,

Alternative Hypothesis, Ha: There is significant difference between means of several groups

and the Test-Statistics: Under Ho,

  

We will reject Ho and conclude that there is significant difference between means of several groups when F value is significantly too large and for that to happen, MS Between Groups should be large enough as compared to MS within Groups.

Answer 7. c. 1

Explanation:

We have, Total Sum of Squares = Sum of Squares due to Regression + Sum of Squares due to Residuals

If all the points lie on the Fitted Regression Line, then the residuals are all 0 which means Sum of Squares due to Residuals are also 0. Therefore, Total Sum of Squares = Sum of Squares due to Regression.

Now,

Answer 8. d. all of the above

Explanation:

Width of the Prediction Interval =

  

which includes standard error of estimate = , value of X to be predicted = x0 and sample size n.

Answer 9. d. minimizes the sum of the squared vertical distances between each observation and the line.

Explanation:

The Estimated Regression line is obtained by estimating the parameters of regression using Principle of Least Squares i.e. by minimizing Error Sum of Squares which are nothing but the the sum of the squared vertical distances between each observation and the line.