Question

Bought	Income	Children	ViewedAd
0	37.00	2	2
1	47.00	1	1
0	47.00	1	2
0	49.00	2	2
1	59.00	1	1
0	13.00	2	1
0	51.00	1	2
0	38.00	1	2
0	60.00	1	1
1	48.00	1	1
0	17.00	1	2
0	60.00	2	2
0	38.00	1	1
0	24.00	1	2
0	15.00	1	2
1	59.00	1	2
0	28.00	1	2
0	36.00	1	2
0	10.00	2	1
0	46.00	2	2
1	55.00	1	1
0	37.00	1	1
1	13.00	1	1
0	55.00	1	2
1	34.00	1	2
0	24.00	1	2
0	19.00	1	2
0	55.00	1	1
0	53.00	1	1
1	57.00	1	1
0	30.00	2	1
0	53.00	1	2
0	60.00	1	1
1	51.00	1	1
1	23.00	1	1
0	53.00	1	1
0	43.00	1	2
0	35.00	1	1
0	33.00	2	1
0	30.00	1	2
0	34.00	1	2
0	43.00	2	2
0	36.00	1	2
1	44.00	1	1
0	60.00	1	1
0	56.00	1	2
0	60.00	1	1
1	11.00	1	2
0	33.00	1	2
1	22.00	2	2
1	45.00	1	1
1	55.00	1	2
1	60.00	1	1
0	20.00	2	2
0	15.00	2	1
0	10.00	2	2
1	44.00	1	1
0	25.00	2	2
0	15.00	1	1
1	38.00	1	1
0	10.00	2	2
0	15.00	2	1
1	42.00	1	1
1	33.00	1	2
0	24.00	1	2
0	15.00	2	1
0	24.00	1	1
1	52.00	2	2
0	21.00	2	2
0	21.00	2	2
1	30.00	1	1

SHOW ALL STEPS and ANSWER ALL SECTIONS. Using the spreadsheet above and import it into Minitab to answer the following:

1. Fit a binary logistic model to the data and report your results

a. What are the odds of a consumer who viewed the advertisement buying the cereal compared to a consumer who did not view the advertisement?

b. What are the odds of a consumer who has children buying the cereal compared to a consumer who does not have children?

c. Does the model fit the data well? Explain.

d. Is there evidence that the model does not fit the data well? Explain.

Answer 1

The logostic regression is performed in minitab by following steps,

Step 1: Write the data values in worksheet. The screenshot is shown below,

Step 2: Click Stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model. The screenshot is shown below,

Step 3: Select Response in binary responses/frequency format, Response: Bought column, Response event: 1, Continuous predictors: Income, Categorical: Children and ViewedAd column. The screenshot is shown below,

The result is obtained. The screenshots are shown below,

From the result summary obtained above,

Odds Ratios for Categorical Predictors

Level A	Level B	Odds Ratio	95% CI
Children
2	1	0.2387	(0.0445, 1.2788)
ViewedAd
2	1	0.3555	(0.1159, 1.0904)

Odds ratio for level A relative to level B

a)

odds of a consumer who viewed the advertisement buying the cereal compared to a consumer who did not view the advertisement is,

b)

Odds of a consumer who has children buying the cereal compared to a consumer who does not have children is,

c)

The R square value (Deviance)= 12.66% which mean model describle only the 12.65% variance of the data points. Which is not a good fit model.

d)

The P-value (Deviance )=0.194 (from Goodness of fit tests) which is greater than 0.05 at 5% significance level. Hence there is a statistical evidence that the model doesnt fit the data well.