Question

Apple is interested in learning how potential customers view its newest product rollout. To do this, it collected surveys gauging respondents' perceived likelihood of purchase (out of 100), along with their age and income levels. Using these data, describe using regression how the likelihopod of purchase relates to age and income.

Respondent Number	Likelihood	Age (Years)	Income ($)
1	13	70	96,345
2	30	51	73,096
3	74	34	74,180
4	74	61	78,325
5	54	64	95,851
6	61	62	119,116
7	43	70	98,425
8	4	27	69,385
9	52	69	80,768
10	46	50	57,102
11	75	24	63,703
12	84	25	62,667
13	66	47	69,375
14	32	63	88,791
15	30	56	73,974
16	96	34	64,727
17	63	56	74,500
18	16	20	43,648
19	90	21	64,475
20	60	42	67,863

Answer 1

The regression equation can be given as

Intercept shows the impact of factors other than chosen independent variables on the dependent variables.

58.21 ------> It shows that to a very large extent factors other than age and income impact the likelihood of purchase.

-0.6454 -------> it means that for a unit increase in age, purchase likelihood decreases by 0.6454

0.0000335871 -----------> it means for a unit increase in income the purchase likehood will increase by 0.00003 or it mean a negligible impact

Also it must be noted that p- value for both age and income is >0.05 so it is advisable to discard these variables and run the regression again because these do not impact the purchase likelihood. This can also be explained with the help of the R2 and significance f value given below

	Coefficients	P-value
Intercept	58.21423377	0.053993395
AGE	-0.645423812	0.234212915
INCOME	0.000335871	0.541871983

R2= 0.09303

The explanatory variables impact the dependent variable hihly when R2 value is closer to 1. This value obtained says that on 9% purchase likelihood is explained by age and income

Significance F= 0.436025

If F > 0.05 it is better to discard independent variables with high p- value (>0.05) and run the regression again till significance F drops below 0.05