Calculate the Pearson chi- square goodness-of-fit test by hand for the Cancercells data.
a. Complete Table 7.4 by using the logistic regression model from Question 26 to calculate the expected (predicted) cell counts.
Table 7.4 Observed and expected values using the logistic regression model for the Cancercells data, where i is estimated from the logistic regression model [i = eb0+ b1xi/(1 + eb0+ b1xi)].

b. Calculate the Pearson chi-square test statistic:
x2 = ˆ‘(observed count €“ expected count)2 / expected count (7.25)
Using the observed count and expected count from Table 7.4. There are 10 observed and 10 expected cells.
c. Find the p-value by using software or looking up the statistic in a chi-square probability distribution table.
d. Interpret the results and clearly state how your conclusions are impacted by random sampling and random allocation to treatments in the original study design. Remember that a small p-value pro-vides evidence that the model is not a good fit.

Transcribed Image Text:

Observed Expected iradius Benign Malignant Total Benign 1 2.5 Malignant Total 115(m) 115(0.00898) 113 15 115(1 115 = 113.967 1 .033 2 3.5 140 85 17 12 34 43 121 212 152 119 60 123 569 | 152 119 60 123 569 152π:"16. 13 4 4.5 5 6.5 Total 357 357 212