# MATHEMATICS

15. Exhibit 14-1

A regression analysis resulted in the following information regarding a dependent variable (*y*) and an independent variable (*x*).

*n* = 10

S*x* = 55

S*y* = 55

S*x*^{2} = 385

S*y*^{2 }= 385

S*xy* = 220

Refer to Exhibit 14-1. The point estimate of *y* when *x* = 20 is

[removed] | 0 | |

[removed] | 31 | |

[removed] | 9 | |

[removed] | -9 |

Coefficient of determination = +1

16. Exhibit 14-1A regression analysis resulted in the following information regarding a dependent variable (*y*) and an independent variable (*x*).

Sum (x) = 30

Sum (x^{2}) = 104

Sum (y) = 40

Sum (y^{2}) = 178

Sum (x)(y) = 134

n=10

Refer to Exhibit 14-1. Interpret the y-intercept.

[removed] | The estimated value of x is 1 if y is 0. | |

[removed] | The estimated value of y is 1 if x is 0. | |

[removed] | The estimated increase in y is 1 for each additional unit of x. | |

[removed] | The estimated increase in x is 1 for each addition unit of y. |

17. You are given the following information about *y* and *x*.

y |
x |

Dependent Variable |
Independent Variable |

5 | 15 |

7 | 12 |

9 | 10 |

11 | 7 |

Refer to Exhibit 14-2. The least squares estimate of *b*_{0} equals

[removed] | -7.647 | |

[removed] | -1.3 | |

[removed] | 21.4 | |

[removed] | 16.41176 |

18. Exhibit 14-2You are given the following information about *y* and *x*.

y |
x |

Dependent Variable |
Independent Variable |

5 | 15 |

7 | 12 |

9 | 10 |

11 | 7 |

Refer to Exhibit 14-2. The coefficient of determination equals

[removed] | -0.99705 | |

[removed] | -0.9941 | |

[removed] | 0.9941 | |

[removed] | 0.99705 |

19. Exhibit 14-3

Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.

y cap = 12 + 1.8 *x
n* = 17

SSR = 225

SSE = 75

*s*

_{b1}= 0.2683

Refer to Exhibit 14-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is

[removed] | $66,000 | |

[removed] | $5,412 | |

[removed] | $66 | |

[removed] | $17,400 |

20. Exhibit 14-3

Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.

y cap = 12 + 1.8 *x
n* = 17

SSR = 225 SSE = 75

*s*

_{b1}= 0.2683

Refer to Exhibit 14-3. The *t* statistic for testing the significance of the slope is

[removed] | 1.80 | |

[removed] | 1.96 | |

[removed] | 6.709 | |

[removed] | 0.555 |

21. The following results were obtained as a part of simple regression analysis:

r^{2} = .9162

F statistic from the Ftable = 3.59

Calculated value of F from the ANOVA table = 81.87

alpha = .05

p-value = .0000

The null hypothesis of no relationship between the dependent variable and the independent variable

[removed] | is rejected | |

[removed] | cannot be tested with the given information | |

[removed] | is not rejected | |

[removed] | is not an appropriate null hypothesis for this situation |

22. The degrees of freedom error (within group variation) of a completely randomized design (one way ANOVA) test with four groups (treatments) and 15 observations per each group is:

[removed] | 3 | |

[removed] | 56 | |

[removed] | 59 | |

[removed] | 14 | |

[removed] | 4 |

23. When computing an individual confidence interval using t statistic for comparing more than two means and if we do all possible pairwise comparisons of means, the experimentwise error rate will be

[removed] | equal to alpha | |

[removed] | less than alpha | |

[removed] | greater than alpha | |

[removed] | may be less than or greater than alpha |

24. After analyzing a data set using one-way analysis of variance, the same data is analyzed using a two factor, full factorial design ANOVA model with two observations per cell. The F statistic for the treatment in the one way ANOVA is ______________________ smaller than the F statistic for treatment in the two-factor full factorial design ANOVA model.

[removed] | always | |

[removed] | sometimes | |

[removed] | never | |

[removed] |

25. In a latin Squares design ANOVA with 6 treatments, total degrres of freedom and degrees of freedom error are:

[removed] | 36,21 | |

[removed] | 15,10 | |

[removed] | 35,20 | |

[removed] | 35,5 | |

[removed] | 36,6 |

26. Which of the following is not a major assumption of the simple regression model:

[removed] | Independence of error terms | |

[removed] | Nominal data | |

[removed] | Normal distribution of the variables | |

[removed] | Equal (constant) variances |