Question

( PARTS 5-8 Only )

1.Generate a scatter plot for CREDIT BALANCE vs. SIZE, including the graph of the "best fit" line. Interpret.

2.Determine the equation of the "best fit" line, which describes the relationship between CREDIT BALANCE and SIZE. Interpret the values for slope and intercept.

3.Determine the coefficient of correlation. Interpret.

4.Determine the coefficient of determination. Interpret.

5. Test the utility of this regression model (use a two tail test with α=.05) by setting up the appropriate test of hypothesis. Interpret your results, including the p-value.

6. Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE? Explain.

7.Compute the 98% confidence interval for β1 (the population slope). Interpret this interval.

8. What can we say about the credit balance for a customer that has a household size of 9 ? Explain your answer.

Location	Income ($1000)	Size	Years	Credit Balance ($)
Urban	54	3	12	4,016
Rural	30	2	12	3,159
Suburban	32	4	17	5,100
Suburban	50	5	14	4,742
Rural	31	2	4	1,864
Urban	55	2	9	4,070
Rural	37	1	20	2,731
Urban	40	2	7	3,348
Suburban	66	4	10	4,764
Urban	51	3	16	4,110
Urban	25	3	11	4,208
Urban	48	4	16	4,219
Rural	27	1	19	2,477
Rural	33	2	12	2,514
Urban	65	3	12	4,214
Suburban	63	4	13	4,965
Urban	55	6	15	4,412
Urban	21	2	18	2,448
Rural	44	1	7	2,995
Urban	37	5	5	4,171
Suburban	62	6	13	5,678
Urban	21	3	16	3,623
Suburban	55	7	15	5,301
Rural	42	2	19	3,020
Urban	41	7	18	4,828
Suburban	54	6	14	5,573
Rural	30	1	14	2,583
Urban	48	2	8	3,866
Urban	34	5	5	3,586
Suburban	67	4	13	5,037
Rural	50	2	11	3,605
Urban	67	5	1	5,345
Urban	55	6	10	5,370
Urban	52	2	11	3,890
Urban	62	3	2	4,705
Urban	64	2	6	4,157
Suburban	22	3	18	3,899
Urban	29	4	4	3,890
Suburban	39	2	18	2,972
Rural	35	1	11	3,121
Urban	39	4	15	4,183
Suburban	54	3	9	3,730
Suburban	23	6	18	4,127
Rural	27	2	1	2,921
Urban	26	7	17	4,603
Suburban	61	2	14	4,273
Rural	30	2	14	3,067
Rural	22	4	16	3,074
Suburban	46	5	13	4,820
Suburban	66	4	20	5,149
Rural	53	1	7	2845
Urban	44	6	5	3962
Suburban	74	7	12	5394
Urban	25	3	15	3442
Suburban	66	7	14	5036

Answer 1

1.Generate a scatter plot for CREDIT BALANCE vs. SIZE, including the graph of the "best fit" line. Interpret.

Select Size and credit balance data and go to insert tab --> select scatter plot diagram

- select one of the data point and right click " add trend line"

- In the right side format trendline option "select display an equation chart " and select r-squared value"

2.Determine the equation of the "best fit" line, which describes the relationship between CREDIT BALANCE and SIZE. Interpret the values for slope and intercept.

we have already brought best fit line and equation of slope and intercept

y = 385.06x + 2620.3

3.Determine the coefficient of correlation. Interpret.

=CORREL(C3:C57,D3:D57)

r =0.7632

4.Determine the coefficient of determination. Interpret.

R² value also we got it in the scatterplot diagram.

simple way to calculate is "r *r"

r-squared = 0.7632 * 0.7632

= 0.5825

5. Test the utility of this regression model (use a two tail test with α=.05) by setting up the appropriate test of hypothesis. Interpret your results, including the p-value.

Significance F is the p value

A p-value is the probability of seeing something as extreme as was observed, if the model were true." In hypothesis testing, when your p-value is less than the alpha level you selected (typically 0.05), you'd reject the null hypothesis in favor of thealternative hypothesis.

6. Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE? Explain.

R-squared value 0.5 < r < 0.7 this value is generally considered a Moderate effect size. So r -squared value 0.58 would tell us the size and credit balance are having moderate effect size.

Best fit also clearly says the trend is between sze and credit balance would be positive linear relationship

7.Compute the 98% confidence interval for β1 (the population slope). Interpret this interval.

find mean, standard deviation and sample size for the credit balance

What can we say about the credit balance for a customer that has a household size of 9 ?

Since the maximum value of the predictor variable (size) used to formulate the given regression model is 7, which is much less than 9, hence we cannot use the given regression model to accurately estimate the credit balance for a customer that has a household size of 9.