• Internal Code :
  • Subject Code : ECONS205
  • University :
  • Subject Name : Statistics

Data Analytics with Business Applications

Outline the key statistics for each of the variables, by using the descriptive statistics function in Data Analysis in Excel. Briefly describe each variable by referring to 3 or 4 of the statistics presented in the table. (Hint: Present the table showing all the statistics identified in the 1st column and then paste in the relevant information for each variable). (10 marks)

 

Statistics

LSpend

Educ

Age

# Child

Inc

Mean

5.390

12.780

43.330

1.780

32.920

Standard Error

0.379

0.336

1.199

0.132

1.567

Median

6.500

12

42.500

2

28

Mode

0

11

53

3

22

Standard Deviation

3.787

3.356

11.988

1.323

15.670

Sample Variance

14.341

11.264

143.718

1.749

245.549

Kurtosis

-1.192

-1.060

0.544

0.000

3.413

Skewness

-0.203

0.200

0.492

0.416

1.813

Range

13

13

61

6

84

Minimum

0

7

21

0

11

Maximum

13

20

82

6

95

Sum

539

1278

4333

178

3292

Count

100

100

100

100

100

LSpend:

  • Form the variable LSpend, it has shown that approximately 5% of their total household income is spent by adults on Lottery
  • 23 adults out of 100, do not spend on lottery as shown in the analysis. Though the maximum value spent is 13% of their total household income.
  • Median is 6.5 which represents that the exactly 50% of the adults either do not spent or spend less than 6.5% of total household income and rest 50% of adults spend more than 6.5% of household income

Education:

  • Form the variable Education, it has shown that approximately 12 years of education is having by adults in the sample.
  • Since the median is 12, we can say that 50 per cent of adults are having 7 to 12 number of years of education whereas rest 50 percent is having between 12 to 20 years of experience

Age:

  • Sample mean age is around 43 years and median is also approximataely 43 which means that 50% of adults age lies between 21 to 43 and rest lies between 43 till 82
  • If you compare the median, minimum and maximum value, you will get to know that older people buy more lottery than younger people
  • Skewness value is approximately 0.5 which shows that the data is moderately skewed

Child:

  • People who spend on lotteries are having on an average 2 child.
  • Since the minimum value is zero also, which represents people without child also buy lotteries
  • People with more number of children spend less as compared to people having less children’s

Income:

  • Average income of adults is approximately 33 thousand dollars who buy lotteries
  • Data is heavily skewed as the value of Skewness is 1.813.
  • Kurtosis value is 3.14, which is more than +1, and then the distribution is too peaked. Likewise, a kurtosis of less than -1 indicates a distribution that is too flat.
  • Use Excel to draw a separate scatter plot for each independent variable against the dependent variable (i.e. amount spent on lotteries as a % of total income LSpend). Include the linear trend line for each graph. Using only the information from the graphs, which independent variable appears to have the strongest linear relationship with proportion of total income spend on lotteries? Briefly discuss if any of the belief’s i) to iv) are confirmed by the plots? (14 marks)

Using only the information from the graphs, which independent variable appears to have the strongest linear relationship with proportion of total income spend on lotteries? Briefly discuss if any of the belief’s i) to iv) are confirmed by the plots?

Among the all 4 independent variable, Education shows the strongest linear relationship with the total income spend on lotteries. Coefficient sign is negative which shows the negative relationship, means uneducated people spend more on lotteries than relatively educated people.

Similarly, it is shown from the 4th Chart, that poor people spend a greater proportion of their income on lotteries than relatively rich people, as the graph shows the downward direction.

  • [10 marks] (i) Develop a simple regression for each of the independent variables against the dependent variable and summarise the results in the table below. Include the p-value underneath each coefficient.

Statistics

Model (1)
Education

Model (2)
Age

Model (3)
# Child

Model (4)
Personal Income

Intercept

14.334

2.972

5.507

10.077

Coefficients

-0.700

0.056

-0.066

-0.142

(p-value)

0.000

0.079

0.820

0.000

R-Square

38.47%

3.12%

0.05%

34.70%

Significance-F

0.000

0.079

0.820

0.000

(ii) Use this information to discuss which model is the best. Give an interpretation of the best equation.

According to the summary table, Model 1 and Mode 2 represent the best as compared to others. Because the RSquare value is higher in these two cases which represents the % variation in dependent variable is explained by the independent variable.

Similarly, p-value for model 1 and 3 are very negligible as compared to Model 2 & 3 (higher than 0.05)

Coefficient signs also indicate that the relationship with depdent variable. In model 1 and Model 4, both the coefficients are negative which means spend on lotteries decreases with the more education and rich people.

(iii) Discuss if the four beliefs are confirmed by their appropriate simple regression equation.

Model 2 and Model 3 are not giving significant results as their p-value is graeter than 0.05 and their R-Square value is very less which represents that the variation in dependent variable is not captured by the independent variable.

Both model 1 and model 4 are confirmed by the simple regression equation as explained in previous part.

Remember, at the center of any academic work, lies clarity and evidence. Should you need further assistance, do look up to our Statistics Assignment Help

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