Question

Purchase	Income ($ '000)	Age	Gender
0	71.9	42	2
0	100.4	42	1
0	105.6	44	1
1	83.1	39	2
0	114.2	43	1
1	113.5	44	1
0	115.2	42	1
0	100.4	35	2
0	92.6	43	2
0	123.8	42	1
0	122.8	45	1
1	98.6	46	2
0	107.6	41	2
0	108.4	42	2
1	138.8	41	1
1	109.9	44	2
1	136.2	47	1
1	117.6	38	2
1	122.8	43	2
0	121.8	45	2
1	126.6	41	2
1	125.8	46	2
1	138.8	42	2
0	149.6	37	1
1	159.5	33	2

Code definitions: Purchase 0 – Not purchased and 1 – Purchased;   Gender 1 – Male and 2 – Female

Fit a logistic regression model to predict purchase decision. Identify significant predictors and comment on classification accuracy.

Submit a word doc including key results and their interpretation for both parts A and B. Attach Excel files to support your results which is a must to get credit for the assignment.

Answer 1

Data:

Purchase	Income	Age	Gender
0	71.9	42	2
0	100.4	42	1
0	105.6	44	1
1	83.1	39	2
0	114.2	43	1
1	113.5	44	1
0	115.2	42	1
0	100.4	35	2
0	92.6	43	2
0	123.8	42	1
0	122.8	45	1
1	98.6	46	2
0	107.6	41	2
0	108.4	42	2
1	138.8	41	1
1	109.9	44	2
1	136.2	47	1
1	117.6	38	2
1	122.8	43	2
0	121.8	45	2
1	126.6	41	2
1	125.8	46	2
1	138.8	42	2
0	149.6	37	1
1	159.5	33	2

> model = glm(Purchase~Income+Age+Gender,data=data,family = "binomial")
> summary(model)

Call:
glm(formula = Purchase ~ Income + Age + Gender, family = "binomial",
data = data)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.9208 -0.7992 -0.4139 0.8686 1.9216

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -17.66520 9.26768 -1.906 0.0566 .
Income 0.06139 0.03015 2.036 0.0417 * (significant)
Age 0.16189 0.15741 1.028 0.3037
Gender 2.28756 1.11809 2.046 0.0408 *(significant)
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 34.617 on 24 degrees of freedom
Residual deviance: 26.600 on 21 degrees of freedom
AIC: 34.6

Number of Fisher Scoring iterations: 4

Here,

• Income is significant to purchase as p-value < 0.05
• Gender is also significant to purchase as p-value < 0.05
• Intercept and Age are not significant as p-value > 0.05.
• AIC = 34.6 is a low value meaning that model is good fit
• This model fit is appropriate and we can predict purchase with help of Age and Gender

Please rate my answer and comment for doubt.