Question: 1

A student is interested in studying the impact of the number of books students referred to in a statistics course and the number of lectures they attended on the final grade on the course. A sample of 30 students is selected and the data are given below:

BOOKS	ATTEND	GRADE
2	17	60
3	18	54
1	17	62
5	20	59
2	12	44
1	13	40
3	17	96
4	19	90
5	22	97
2	22	54
5	22	91
1	12	48
3	18	91
1	12	65
4	21	82
5	14	61
3	18	54
3	13	46
1	8	64
5	22	90
1	12	48
3	18	91
3	13	54
1	17	91
4	19	48
5	22	91
3	22	65
3	22	82
1	12	61

using Excel, develop an estimated regression equation using the number of books referred to and the number of lectures attended to predict the final grade on the course.

Joseph referred to 4 books and attended 19 lectures. What is his predicted final score on the course?

74.51

78.82

79.94

85.67

65.93

Question: 2

A student is interested in studying the impact of the number of books students referred to in a statistics course and the number of lectures they attended on the final grade on the course. A sample of 30 students is selected and the data are given below:

BOOKS	ATTEND	GRADE
2	17	60
3	18	54
1	17	62
5	20	59
2	12	44
1	13	40
3	17	96
4	19	90
5	22	97
2	22	54
5	22	91
1	12	48
3	18	91
1	12	65
4	21	82
5	14	61
3	18	54
3	13	46
1	8	64
5	22	90
1	12	48
3	18	91
3	13	54
1	17	91
4	19	48
5	22	91
3	22	65
3	22	82
1	12	61

using Excel, develop an estimated regression equation using the number of books referred to and the number of lectures attended to predict the final grade on the course.

Use theFtest to determine the overall significance of the relationship. What is your conclusionat the 0.05 level of significance?

Thepvalue associated with theFtest for an overall regression relationship is 6.267.

Because thispvalue of 6.267 is higher than the 0.05 level of significance, we failed to reject the hypothesisthat1=2 = 0.

Thepvalue associated with theFtest for an overall regression relationship is 0.006.

Because thispvalue is less than the 0.05 level of significance, we reject the hypothesisthat1=2 = 0.

Thepvalue associated with theFtest for an overall regression relationship is 6.267.

Because thispvalue of 6.267 is higher than the 0.05 level of significance, we reject the hypothesisthat1=2 = 0.

Thepvalue associated with theFtest for an overall regression relationship is 0.052.

Because thispvalue is higher than the 0.05 level of significance, we fail to reject the hypothesisthat1=2 = 0.

Thepvalue associated with theFtest for an overall regression relationship is 0.707.

Because thispvalue is higher than the 0.05 level of significance, we fail to reject the hypothesisthat1=2 = 0.

Thepvalue associated with theFtest for an overall regression relationship is 0.00012.

Because thispvalue is lower than the 0.05 level of significance, we reject the hypothesisthat1=2 = 0.

Question: 3

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age are related to annual income. A sample of 30 employees is selected and the data are given below.

Education (No. of years)	Length of tenure in current employment (No. of years)	Age (No. of years)	Annual income ($)
17	8	40	124.000
12	12	41	30.000
20	9	44	193.000
14	4	42	88.000
12	1	19	27.000
14	9	28	43.000
12	8	43	96.000
18	10	37	110.000
16	12	36	88.000
11	7	39	36.000
16	14	36	81.000
12	4	22	38.000
16	17	45	140.000
13	7	42	11.000
11	6	18	21.000
20	4	40	151.000
19	7	35	124.000
16	12	38	48.000
12	2	19	26.000
10	6	44	124.000
18	9	39	108.000
14	5	38	109.000
12	7	29	114.000
24	12	54	100.000
26	11	48	98.000
18	10	45	134.000
15	9	49	127.000
13	7	39	122.000
14	8	40	122.001
15	9	41	122.002

using Excel, develop an estimated regression equation using the Education (No. of years), Length of tenure in current employment (No. of years) and Age (No. of years) to predict the Annual Income. Check the regression output table in Excel and remove all independent variables that are not significant at the 0.05 level of significance from the estimated regression equation.

What is your estimated regression equation after removing the statistically insignificant variables?

Predicted Annual Income = -18,955.2+ 2,941.3*Age

Predicted Annual Income = 510.163+5,553.523*Education+752.347*Length of Tenure

Predicted Annual Income = -18,799.1 -1,192.13*Length of Tenure +3196.67*Age

Predicted Annual Income = 32,345.564+ 123.867*Education

Predicted Annual Income = -24,567.13+ 69.13*Length of Tenure

Question: 4

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age are related to annual income. A sample of 30 employees is selected and the data are given below.

Education (No. of years)	Length of tenure in current employment (No. of years)	Age (No. of years)	Annual income ($)
17	8	40	124.000
12	12	41	30.000
20	9	44	193.000
14	4	42	88.000
12	1	19	27.000
14	9	28	43.000
12	8	43	96.000
18	10	37	110.000
16	12	36	88.000
11	7	39	36.000
16	14	36	81.000
12	4	22	38.000
16	17	45	140.000
13	7	42	11.000
11	6	18	21.000
20	4	40	151.000
19	7	35	124.000
16	12	38	48.000
12	2	19	26.000
10	6	44	124.000
18	9	39	108.000
14	5	38	109.000
12	7	29	114.000
24	12	54	100.000
26	11	48	98.000
18	10	45	134.000
15	9	49	127.000
13	7	39	122.000
14	8	40	122.001
15	9	41	122.002

using Excel, develop an estimated regression equation using the Education (No. of years), Length of tenure in current employment (No. of years) and Age (No. of years) to predict the Annual Income.

Annual Income=0 +1*Education +2*Length of Tenure+3*Age

Use thettest to determine the significance of each independent variable.

Which of the following statements CANNOT be said from thettest results at the 0.05 level of significance?

Thepvalue associated with the estimated regression parameterb1 for Education is 0.14.Because thispvalue is higher than the 0.05 level of significance, we fail to reject the hypothesis that1= 0.

Thepvalue associated with the estimated regression parameterb2for Length of Tenure is 0.45.Because thispvalue is higher than the 0.05 level of significance, we fail to reject the hypothesis that2= 0.

Thepvalue associated with the estimated regression parameterb3for Age is 0.02.Because thispvalue is lower than the 0.05 level of significance, we fail to reject the hypothesis that3= 0. Hence, we cannot conclude that there is a relationship between age andthe annual income at the 0.05 level of significance when controlling for education level and length of tenure in current employment.

Thepvalue associated with the estimated regression parameterb2for Length of Tenure is 0.45.Because thispvalue is higher than the 0.05 level of significance, we cannot conclude that there is a relationship between the length of tenure in current employment andthe annual income at the 0.05 level of significance when controlling for education level and age.

Question: 5

Consider the following data with the dependent variabley, independent variablex, and the dummy variabled.

Y	d	x
100	0	9,3
100	0	6,5
50	0	4,2
75	1	7,4
65	0	6
90	0	7,6
85	1	9,6
65	1	6,5
50	1	6
75	1	9,9
75	1	8,6
65	0	4,9
95	0	7,2
95	0	9,9
90	1	7,8
80	1	7,2
75	0	7
95	0	8,7
100	1	9,9
90	1	9,3
70	1	9,1
100	0	8,9
40	0	5,4
90	0	8,8
75	1	8,8
40	1	5
45	1	6,5
55	0	5,2
100	0	10
90	0	8,4
80	1	6,4
80	0	6,7
90	1	8,5
60	0	5,9
95	1	8,9
45	0	6,3
65	0	7,5
85	1	6,8
60	1	5,7
75	1	4,5

using Excel, develop the estimated regression equation using all of the independent variables included in the data.

Test for an overall regression relationship at the 0.05 level of significance. Is there a significant regression relationship?

Thepvalue associated with theFtest for an overall regression relationship is 7.813E-07 = 0.0000007813, which is essentially zero.

Because thispvalue is less than the 0.05 level of significance, we reject the hypothesis that1 =2 = 0and conclude that there is an overall regression relationship at the 0.05 level of significance.

Thepvalue associated with theFtest for an overall regression relationship is 7.813E-07 = 0.0000007813, which is essentially zero.

Because thispvalue is less than the 0.05 level of significance, we fail to reject the hypothesis that1 =2 = 0and conclude that there is NO evidence of overall regression relationship at the 0.05 level of significance.

Thepvalue associated with theFtest for an overall regression relationship is 0.154

Because thispvalue is higher than the 0.05 level of significance, we fail to reject the hypothesis that1 =2 = 0and conclude that the model is wrong.

Thepvalue associated with theFtest for an overall regression relationship is 0.154

Because thispvalue is higher than the 0.05 level of significance, we reject the hypothesis that1 =2 = 0and conclude that the model is perfect.

Question: 6

A health science-kinesiology program to lose weight collected data from ten students. Sex was coded as 1=female and 0=male. The regression equation obtained by using a statistical software was:

Pounds lost = 15.8 + 0.65 time + 6.00 sex

For the same length of time in the program, the weight loss of a female compared to a male is:

19.05 more pounds.

15.8 less pounds.

3.25 more pounds.

6 more pounds.

Question: 7

What factors affect the sale price of oceanside condominium units?

To answer this question, the following data were recorded for each of the n = 105 units sold at auction:

y = sale price (in thousands of dollars)

x1 = floor height (1, 2, 3, ..., 8)

x2 = 1 is ocean view; 0 is bay view

The least squares prediction equation is y = 17.770 - 0.073 x1 + 3.137 x2.

Interpret the estimated effect of floor height.

Note: Pay attention to the unit of measurements.

Expected sale price increases by $73 for each one floor increase in floor height for the same view type.

Expected sale price decreasesby $73 for each one floor increase in floor height for the same view type.

Expected sale price increases by $0.73 for each one floor increase in floor height for the same view type.

The correlation between selling price and floor height is -0.073.

Expected sale price decreasesby $0.73 for each one floor increase in floor height for the same view type.

Question 8

Suppose statistical software gives the following equation for a logistic regression analysis:

logit(pi) = -4.85 +1.25x1 + 0.85x2

Which of the following choices is closest to the predicted probability for x1 = 3.12 and x2 = 2.41?

0.25

0.5

0.75

0.85

0.95

Question 9

A multiple regression model has the following equation:Y = 7 + 2X1+ 9X2

As x1increases by 1 unit (holding x2constant), Y is expected to...

decrease by 9 units

increase by 7 units

increase by 9 units

increase by 2 units

increase by 18 units

decrease by 2 units

Question: 10

Variable Description Y number of days absent last fiscal year X1 commuting distance (in miles) employee's age (in years) X3 single-parent household (0 = yes, 1 = no) X4 length of employment at PPP (in years) X5 shift (0 = day, 1 = night) Coefficients Standard Error t Statistic p-value Intercept 6.594146 3.273005 2.014707 0.047671 X1 -0.18019 0.141949 -1.26939 0.208391 0.268156 0.260643 1.028828 0.307005 X3 -2.31068 0.962056 -2.40182 0.018896 X4 -0.50579 0.270872 -1.86725 0.065937 X5 2.329513 0.940321 2.47736 0.015584 df SS MS F p-value Regression 5 279.358 55.8716 4.423755 0.001532 Residual 67 846.2036 12.6299 Total 72 1125.562 R = 0.498191 R2 =0.248194 Adj R2 = 0.192089 Se = 3.553858 n = 73