Question
In: Statistics and Probability
Evaluate your model using all factors outlined in the text. Assumptions, conditions, fit, outliers, etc. Then...
Evaluate your model using all factors outlined in the text. Assumptions, conditions, fit, outliers, etc.
Then explain your answer in words. Create a linear regression model that has 2 or 3 independent variables. Your choice of models…your choice of variables.
A1 Tim is a wedding planner. Looking at the data he has accessed, he is trying to simplify a model for how much a wedding will cost. Use the data to create a model with 2 or 3 Independent Variables, to predict Wedding Cost (dependent variable.) Evaluate your model using all factors outlined in the text.
| Couple's Income | Bride's age | Payor | Wedding cost | Attendance | Value Rating | var7 |
| 130000 | 22 | Bride's Parents | 60700 | 300 | 3 | |
| 157000 | 23 | Bride's Parents | 52000 | 350 | 1 | |
| 98000 | 27 | Bride & Groom | 47000 | 150 | 3 | |
| 72000 | 29 | Bride & Groom | 42000 | 200 | 5 | |
| 86000 | 25 | Bride's Parents | 34000 | 250 | 3 | |
| 90000 | 28 | Bride & Groom | 30500 | 150 | 3 | |
| 43000 | 19 | Bride & Groom | 30000 | 250 | 3 | |
| 100000 | 30 | Bride & Groom | 30000 | 300 | 3 | |
| 65000 | 24 | Bride's Parents | 28000 | 250 | 3 | |
| 78000 | 35 | Bride & Groom | 26000 | 200 | 5 | |
| 73000 | 25 | Bride's Parents | 25000 | 150 | 5 | |
| 75000 | 27 | Bride & Groom | 24000 | 200 | 5 | |
| 64000 | 25 | Bride's Parents | 24000 | 200 | 1 | |
| 67000 | 27 | Groom's Parents | 22000 | 200 | 5 | |
| 75000 | 25 | Bride's Parents | 20000 | 200 | 5 | |
| 67000 | 30 | Bride's Parents | 20000 | 200 | 5 | |
| 62000 | 21 | Groom's Parents | 20000 | 100 | 1 | |
| 75000 | 19 | Bride's Parents | 19000 | 150 | 3 | |
| 52000 | 23 | Bride's Parents | 19000 | 200 | 1 | |
| 64000 | 22 | Bride's Parents | 18000 | 150 | 1 | |
| 55000 | 28 | Bride's Parents | 16000 | 100 | 5 | |
| 53000 | 31 | Bride & Groom | 14000 | 100 | 1 | |
| 62000 | 24 | Bride's Parents | 13000 | 150 | 1 | |
| 40000 | 26 | Bride's Parents | 7000 | 50 | 3 | |
| 45000 | 32 | Bride & Groom | 5000 | 50 | 5 |
Solutions
Expert Solution
The regression has five key assumptions:
- Linear relationship
- Multivariate normality
- No or little multicollinearity
- No auto-correlation
- Homoscedasticity
The assumptions are met.
The regression output is:
| R² | 0.734 | ||||
| Adjusted R² | 0.710 | ||||
| R | 0.857 | ||||
| Std. Error | 7126.932 | ||||
| n | 25 | ||||
| k | 2 | ||||
| Dep. Var. | Wedding cost | ||||
| ANOVA table | |||||
| Source | SS | df | MS | F | p-value |
| Regression | 3,08,93,12,887.3528 | 2 | 1,54,46,56,443.6764 | 30.41 | 4.65E-07 |
| Residual | 1,11,74,49,512.6472 | 22 | 5,07,93,159.6658 | ||
| Total | 4,20,67,62,400.0000 | 24 | |||
| Regression output | confidence interval | ||||
| variables | coefficients | std. error | t (df=22) | p-value | 95% lower |
| Intercept | -7,002.4471 | ||||
| Attendance | 53.0309 | 27.2962 | 1.943 | .0649 | -3.5779 |
| Couple's Income | 0.3124 | 0.0774 | 4.036 | .0006 | 0.1519 |
The regression model is:
Wedding cost = -7,002.4471 + 53.0309*Attendance + 0.3124*Couple's Income
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