Business Statistics

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M4

Data Analysis Results: Automobile Insurance Preimun & Household income
A. Descriptive Statistics
1. Categorical Variable: Gender (D1)
i. & ii. Frequency Distribution and Percentages
Class Freq %
Male 23 51
Female 21 47
Did not answer 1 2
Total 45 100
iii. Bar Chart
iv. Pie Chart
2. Numerical Variable: Insurance Premium (Q5)
i. & ii. Frequency Distribution and Percentages
Class Freq %
< $600 1 14 31.11
< $900 2 9 20.00
< $1200 3 9 20.00
< $1500 4 4 8.89
> $1501 5 9 20.00
Total 45 100
iii. Range 4.00
iv. Mean 2.67
v. Median 2.00
vi. Standard Dev. 1.50
Insurance Premium
Mean 2.6666666667
Standard Error 0.2247332875
Median 2
Mode 1
Standard Deviation 1.5075567229
Sample Variance 2.2727272727
Kurtosis -1.2524651163
Skewness 0.3933671263
Range 4
Minimum 1
Maximum 5
Sum 120
Count 45
B. Inferential Statistics
1. Insurance Premium vs. Houshold Income:
The correlation is positive and with a magnitude of.65 statistically significant (Significance F<.05)
This indicates that if your insurance premium is higher, then it is more likely that your household income is high.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.651403561
R Square 0.4243265993
Adjusted R Square 0.4109388458
Standard Error 1.2611364384
Observations 45
ANOVA
df SS MS F Significance F
Regression 1 50.41 50.41 31.6951308671 0.00000126
Residual 43 68.39 1.5904651163
Total 44 118.8
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.7066666667 0.385283546 1.834147017 0.0735581523 -0.0703316452 1.4836649785 -0.0703316452 1.4836649785
X variable1 0.71 0.1261136438 5.6298428812 0.00000126 0.4556676015 0.9643323985 0.4556676015 0.9643323985
2. Construct a 95% confidence interval (C.I.) for "Insurance Premium"
Using the following formula:
95% C.I. Equals "mean +/- t*Standard Error"
We are using t-score because population standard deviation is unknown
Using t-Table on page 554 in textbook, df=n-1=45-1=44, Upper tail area=.025, we find t=2.015
Mean 2.67
Standard Error. 0.22
t 2.015
95% C.I.
Upper limit 3.11
Lower limit 2.23
In this case we are confident that 95% of similarly constructed intervals will contain the true population mean.
In other words, we are 95% confident that the true population mean will be between 2.23 and 3.11.
Further translation: we are 95% confident that in the population, the average automobile insurance premium tends to be between $900 to $1200 based on the sample we have obtained.
Extra Credit
EC 1-1. Insurance Premium vs. Purchase Price:
The correlation is positive and with a magnitude of.73 statistically significant (Significance F<.05)
This indicates that as your insurance premium rises, more likely your automobile purchase price will increase.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.7290544785
R Square 0.5315204327
Adjusted R Square 0.520625559
Standard Error 1.0437851148
Observations 45
ANOVA
df SS MS F Significance F
Regression 1 53.1520432692 53.1520432692 48.7862869604 0.0000000135
Residual 43 46.8479567308 1.0894873658
Total 44 100
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.9615384615 0.289493904 3.3214463181 0.0018338356 0.3777183711 1.545358552 0.3777183711 1.545358552
X variable1 0.5994591346 0.0858243849 6.9847181017 0.0000000135 0.4263777693 0.7725404999 0.4263777693 0.7725404999
EC 1-2. Purchase Price vs. Household Income:
The correlation is positive and with a magnitude of.56 statistically significant (Significance F<.05)
This indicates that as your automobile purchase price increases, more likely the household income will be high.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.5597515247
R Square 0.3133217694
Adjusted R Square 0.2973525082
Standard Error 1.3773700403
Observations 45
ANOVA
df SS MS F Significance F
Regression 1 37.2226262019 37.2226262019 19.6203046527 0.000063938
Residual 43 81.5773737981 1.8971482279
Total 44 118.8
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1.1730769231 0.3820137158 3.0707717407 0.0036932859 0.4026728523 1.9434809939 0.4026728523 1.9434809939
X variable1 0.5016526442 0.1132531349 4.4294813074 0.000063938 0.2732559334 0.7300493551 0.2732559334 0.7300493551
EC 2. Construct a 95% confidence interval (C.I.) for "Gender"
Using the following formula:
95% C.I. Equals "proportion +/- Z*Standard Error"
We create the confidence interval estimate for the population proportion of male.(categorical data)
We are using z-score; critical value from the standardized norminal distribution. Using z-Table on page 573 in textbook, we find z=1.96
Data
Sample Size 45
Number of Male 23
Confidence level 95%
Intermediate Calculations
Sample Proportion 0.51
Standard Error. 0.07
Z value 1.96
95% C.I.
Upper limit 0.65
Lower limit 0.37
In this case we are confident that 95% of similarly constructed intervals will contain the true population proportion.
In other words, we are 95% confident that the true population proportion will be between 37% and 65%.
Further translation: we are 95% confident that in the population, the actual proportion of male tends to be between 37% to 65% based on the sample we have obtained.

M4
Gender Frequency Distribution
Category
Frequency
Gender Frequency Distribution

M3
Gender Percentages/Proportions
Q1 Q2 Q3 Q4 Q5 Q6 D1 D2
ID NUMBER OF CAR NEW OR USED TYPE OF CAR PURCHASE PRICE ($) INSURANCE PREMIUM($) PER 6 MONTH HOUSEHOLD INCOME ($) GENDER AGE GRP
CODING RULES 1=0 2=1 3=2 4=3+ 1=NEW 2=USED 1=SEDAN 2=SUV 3=SPORTS CAR 4=NONE 5=OTHER 1=<15000 2=<25000 3=<35000 4=<45000 5=<55000 6=>54999 1=<600 2=<900 3=<1200 4=<1500 5=>1499 1=<25000 2=<50000 3=<75000 4=<90000 5=>89999 1=FEMALE 2= MALE 1=15TO24 2=25TO34 3=35TO44 4=45TO54 5=55TO64 6=65+
1 4 1 5 2 2 4 2 1
2 2 2 3 1 5 5 1 1
3 2 2 1 1 1 1 2 2
4 4 2 1,5 2 3 5 1 3
5 3 1,2 1,5 2 2 3 1 6
6 4 1 1,2,5 4 5 4 1 5
7 3 1 1,2 3,6 5 5 2 4
8 4 2 1 1 1 1 1 2
9 2 2 1 1 1 1 2 2
10 1 2 3 1 1 1 1 1
11 2 1 1 3 3 1 1 1
12 3 1 1,2 2 2 5 1 3
13 4 2 1,3 1,2 2 1 2 6
14 2 1 1 2 3 1 1 1
15 2 2 1 1 1 1 2 2
16 4 1 1,3 1,2,3 5 1 1
17 3 1 2 3 3 1 1 2
18 4 2 1 1 1 2 1 1
19 4 1,2 1,2,3 3,5 5 5 1 1
20 4 1,2 1,5 2,3 4 4 1 3
21 1 1 3 3 3 2 2
22 2 2 1 1 1 1 2 1
23 3 2 3 3 5 1 2 1
24 4 2 1 1 2 1 2 1
25 2 1 3 3 3 2 2 2
26 2 1 1 2 2 1 1 2
27 2 2 5 1 1 1 2 2
28 2 1 1 3 3 4 2 2
29 3 1 1,2 3,5 5 5 1 3
30 2 1 3 3 3 2 1 2
31 4 1,2 1,3,5 1,2,3 4 4 1 4
32 1 4 1 1 1
33 3 1 1,3 2,3 4 3 2 5
34 2 1 1 2 3 1 1
35 4 1 1,2,5 4,5 5 5 1 4
36 3 1 1,3 2 1 3 1 1
37 2 1 1 1 1 2 2
38 2 1 1 2 1 2 2 2
39 4 1 1,2 6 5 5 2 4
40 3 1,2 1,3 2 1 3 2 2
41 2 2 3 1 2 1 2 1
42 2 1 1 2 2 1 2 2
43 3 1 1,2 2 4 5 1 4
44 2 1 5 2 2 3 2 2
45 4 1 1 2 1 3 2 2