Question

Is there a relationship between the dollars spent each week on recreation and the number of members of the family? Do larger families spend more on recreation? Ten Chicago families shared the following information:

Family Size 3 6 5 6 6 3 4 4 5 3

Amount Spent 99 104 151 129 142 111 74 91 119 91

h. Predict the recreational spending for a family of size 5.

i. If there are families of that size in the data set, what are the residuals for those observations?

j. Test the explanatory power of the model at a 5% level of significance.

k. Test if there is a positive relationship between family size and recreational spending. Use alpha = 0.01.

l. What is the excel command used to produce the p-value associated with the test in part k?

Answer 1

Chi-Square Test for Association: Worksheet rows, Worksheet columns

Rows: Worksheet rows Columns: Worksheet columns

Family size Amount All

1 3 99 102
3.97 98.03
-0.9706 0.9706
-0.4871 0.0980
-0.5203 0.5203
0.23725 0.00961

2 6 104 110
4.28 105.72
1.7180 -1.7180
0.8302 -0.1671
0.8903 -0.8903
0.68928 0.02792

3 5 151 156
6.07 149.93
-1.0727 1.0727
-0.4353 0.0876
-0.4774 0.4774
0.18947 0.00767

4 6 129 135
5.26 129.74
0.7448 -0.7448
0.3249 -0.0654
0.3526 -0.3526
0.10556 0.00428

5 6 142 148
5.76 142.24
0.2388 -0.2388
0.0995 -0.0200
0.1087 -0.1087
0.00989 0.00040

6 3 111 114
4.44 109.56
-1.4377 1.4377
-0.6825 0.1374
-0.7333 0.7333
0.46579 0.01887

7 4 74 78
3.04 74.96
0.9637 -0.9637
0.5530 -0.1113
0.5842 -0.5842
0.30585 0.01239

8 4 91 95
3.70 91.30
0.3019 -0.3019
0.1570 -0.0316
0.1672 -0.1672
0.02465 0.00100

9 5 119 124
4.83 119.17
0.1730 -0.1730
0.0787 -0.0158
0.0850 -0.0850
0.00620 0.00025

10 3 91 94
3.66 90.34
-0.6592 0.6592
-0.3446 0.0694
-0.3667 0.3667
0.11874 0.00481

All 45 1111 1156

Cell Contents: Count
Expected count
Residual
Standardized residual
Adjusted residual
Contribution to Chi-square

Pearson Chi-Square = 2.240, DF = 9, P-Value = 0.987
Likelihood Ratio Chi-Square = 2.232, DF = 9, P-Value = 0.987

h. The predicted recreational spending of the family of size 5 is 142.24.

i. The residue of the observation having family size 5 is -0.2388.

j. For this data, the Pearson chi-square statistic is 2.240 (p-value = 0.987) and the likelihood ratio chi-square statistic is 2.232 (p-value = 0.987). Both p-values are greater than the significance level of 0.05. Thus, it can be concluded that the variables are not associated and that the dollars spent each week on recreation does not depends on the family size.

k. For this data, the Pearson chi-square statistic is 2.240 (p-value = 0.987) and the likelihood ratio chi-square statistic is 2.232 (p-value = 0.987). Both p-values are greater than the significance level of 0.01. Thus, it can be concluded that there does not exists any relationship between dollars spent each week on recreation and family size.

.