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# Chapter 8, Problem 14

**Using the Excel file Weddings, apply the Excel Regression tool using the wedding cost as the dependent variable and the couple’s income as the independent variable, only for those weddings paid for by the bride and groom. Interpret all key regression results, hypothesis tests, and confidence intervals in the output.**

**Couple's Income**

**Bride's age **

**Payor**

**Wedding cost**

**Attendance**

**Value Rating**

$98,000

27

Bride & Groom

$47,000.00

150

3

$72,000

29

Bride & Groom

$42,000.00

200

5

$90,000

28

Bride & Groom

$30,500.00

150

3

$43,000

19

Bride & Groom

$30,000.00

250

3

$100,000

30

Bride & Groom

$30,000.00

300

3

$78,000

35

Bride & Groom

$26,000.00

200

5

$75,000

27

Bride & Groom

$24,000.00

200

5

$53,000

31

Bride & Groom

$14,000.00

100

1

$45,000

32

Bride & Groom

$5,000.00

50

5

**SUMMARY OUTPUT**

Regression Statistics

Multiple R

0.631021182

R Square

0.398187732

Adjusted R Square

0.312214551

Standard Error

10632.27072

Observations

9

ANOVA

df

SS

MS

F

Significance F

Regression

1

523572624.5

523572624.5

4.631534238

0.068401199

Residual

7

791316264.3

113045180.6

Total

8

1314888889

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

480.4165188

13095.31615

0.036686134

0.971759544

-30485.08564

31445.91867

-30485.08564

31445.91867

Couple's Income

0.373358182

0.173485521

2.15209996

0.068401199

-0.036869887

0.783586252

-0.036869887

0.783586252

PROBABILITY OUTPUT

Predicted Wedding cost

Residuals

Standard Residuals

Percentile

Wedding cost

37069.5184

9930.4816

0.998482042

5.555555556

5000

27362.20566

14637.79434

1.471789122

16.66666667

14000

34082.65294

-3582.65294

-0.360225694

27.77777778

24000

16534.81836

13465.18164

1.353886206

38.88888889

26000

37816.23477

-7816.234765

-0.785900459

50

30000

29602.35475

-3602.354751

-0.362206656

61.11111111

30000

28482.2802

-4482.280204

-0.450680689

72.22222222

30500

20268.40019

-6268.400189

-0.630270039

83.33333333

42000

17281.53473

-12281.53473

-1.234873833

94.44444444

47000

**The estimated regression model is,**

Wedding cost = 480.4165+ 0.3734*Couple's Income

From the above output we can see that the regression model (i.e. the independent variable) is not significant at 0.05 significance level (as p-value = 0.0684 > 0.05). The independent variable is explaining 39.82% (as R-sqr = 0.3982) of the variation in the dependent variable.

As this is a simple regression model and the regression model is not significant so the independent variable is not a significant predictor of the dependent variable.

The slope parameter estimate is 0.3734 implying that per $1 increase in Couple's Income, the expected increase in Wedding cost is $0.3734 on an average.

The 95% confidence interval for the slope is (-0.0369, 0.7836), thus we can be 95% confident that the true slope parameter falls within this interval. As the interval contains value 0 so that is a possible value for population slope indicating that the independent variable is not significant.

**The residual plots are given below,**

The assumptions of linearity and homoscedasticity are not valid.

The scatterplot between wedding cost and couple’s income is showing a random pattern, instead of a linear trend. Therefore, the assumption of linearity is considered invalid. The scatterplot of the wedding cost against the standard residuals is not concentrated near the zero line but are random. Therefore, the assumption of homoscedasticity is also not valid.

**The assumption of normality is not valid.**

If the probability plot of a variable is close to a straight line and doesn’t form any other pattern, the variable follows a normal distribution. However, the probability plot of residuals forms a different pattern than a straight line.

A standard residual is considered an outlier if it is either less than -2 or greater than 2, i.e. 2 times standard deviation of standard residuals which is 1. All the values fall inside this interval. Therefore, all standardized residuals are within ±2 implying that there is no outliers present in the data.

**If a couple makes $80,000 together, their predicted budget is,**

Wedding cost = 480.4165+ 0.3734*80000 = $ 30352.42