1) Tommy's cab company transports riders using 2 routes. Use the following data to determine the mean driving time and the variance in the driving time.
|
Route 1
|
Route 2
|
|
54
|
61
|
|
69
|
62
|
|
58
|
63
|
|
47
|
53
|
|
72
|
58
|
|
56
|
65
|
|
66
|
59
|
|
|
67
|
a) Run Excel descriptive statistics for the data above.
b) Comment on any differences between the data.
2) Use the data in #1 to:
a) Create a hypothesis for the premise that there is no difference in the two samples.
b) Use the F distribution and the Excel (F-test two sample for variance) function to test the hypothesis.
c) Are the populations the same? Why/Why not?
3) Use the following data and run a correlation in Excel.
|
Population
|
Expenditure
|
|
29
|
127
|
|
435
|
214
|
|
86
|
133
|
|
1090
|
208
|
|
219
|
153
|
|
503
|
184
|
|
47
|
130
|
|
3524
|
217
|
|
185
|
141
|
|
98
|
154
|
|
952
|
194
|
|
89
|
103
|
a) Are the data normal? Run Descriptive statistics in Excel and support your answer.
b) Show the results of the correlation in Excel and explain what the results MAY mean.
c) Is there absolutely a relationship between this data? Why, why not?
d) Plot the data on a scatter chart? Does the chart suggest a relationship of the data?
e) Might an outlier have an effect on this data?
f) If there were an outlier, which data point might be the outlier? If you were to remove the outlier how would the correlation and the scatter chart be different?
4) Run a linear regression (in Excel) with the data in the table shown in #3 above. The independent variable is population and the dependent variable is expenditure.
a) Display the regression chart.
b) Comment on the distance of each data point verses the regression line.
c) Does the pattern of points take a cigar-like shape?
d) Are the points far from the line?
e) Is this regression analysis a good predictor of the effect of population on expenditures? Why or why not? Justify your answer.
5) Examine the residuals (get them from Excel) of the regression analysis that you did for #4.
a) Explain how you would get the residuals if Excel did not provide them.
b) Create a table showing each data point and the residual in Excel.
c) Plot the residuals. Show the plot.
d) Comment on the plot. What should the residuals look like?
e) What do they look like?
f) What does this mean regarding the predicting power of the regression for this data?
6) Note: This question is a general question not related to any particular data. What happens to the errors when the regression line is fit on curving data? (Remember the errors are supposed to be normally distributed, have constant variance and not have a pattern, i.e., be independent.)
7) Use the following data to answer the following questions.
|
Skinfold
|
Thigh
|
Midarm
|
Body Fat
|
|
19.5
|
43.1
|
29.1
|
11.9
|
|
24.7
|
49.8
|
28.2
|
22.8
|
|
30.7
|
51.9
|
37
|
18.7
|
|
29.8
|
54.3
|
31.1
|
20.1
|
|
19.1
|
42.2
|
30.9
|
12.9
|
|
25.6
|
53.9
|
23.7
|
21.7
|
|
31.4
|
58.5
|
27.6
|
27.1
|
|
27.9
|
52.1
|
30.6
|
25.4
|
|
22.1
|
49.9
|
23.2
|
21.3
|
|
25.5
|
53.5
|
24.8
|
19.3
|
|
31.1
|
56.6
|
30
|
25.4
|
|
30.4
|
56.7
|
28.3
|
27.2
|
|
18.7
|
46.5
|
23
|
11.7
|
|
19.7
|
44.2
|
28.6
|
17.8
|
|
14.6
|
42.7
|
21.3
|
12.8
|
|
29.5
|
54.4
|
30.1
|
23.9
|
|
27.7
|
55.3
|
25.7
|
22.6
|
|
30.2
|
58.6
|
24.6
|
25.4
|
|
22.7
|
48.2
|
27.1
|
14.8
|
|
25.2
|
51
|
27.5
|
21.1
|
a) Create and display a scatter chart (in Excel) for Body fat (Y axis) and skinfold (x-axis)
b) Create and display a scatter chart (in Excel) for Body fat (Y axis) and thigh (x-axis)
c) Create and display a scatter chart (in Excel) for Body fat (Y axis) and midarm (x-axis)
d) What does each of these charts suggest?
e) Run a correlation for each combination of the data (each independent variable with the dependent variable).
f) What do the correlations for each combination suggest?
8) Run and show linear regressions (in Excel)
a) Body fat as the dependent variable and skinfold as an independent variable.
b) Body fat is the dependent variable and midarm as an independent variable.
c) Body fat as the dependent variable and thigh as an independent variable.
d) Which seems to be a better predictor of the dependent variable body fat. Comment on why you feel this is true.
e) Could this be useful in determining body fat?
9) Run a multiple regression (in Excel) with body fat as the dependent variable and skinfold, midarm and thigh as independent variables. Show the results. Comment on the predictive value of the results.