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Statistics for Economics

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Submitted By spazm85
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Statistical Project Assignment |
Statistics for Business & Economics | |

DATASET 1: SIMPLE REGRESSION ANALYSIS
Variable Definition
Xi = Weight of car (pounds)
Yi = Price of car ($)

1. (a) Regression Model using X to predict Y Weight and Price of Car Sales | | | | | | | | | | | | | Regression Statistics | | | | | | Multiple R | 0.212585295 | | | | | | R Square | 0.045192508 | | | | | | Adjusted R Square | 0.038951936 | | | | | | Standard Error | 7883.368653 | | | | | | Observations | 155 | | | | | | | | | | | | | ANOVA | | | | | | | | df | SS | MS | F | Significance F | | Regression | 1 | 450055137.6 | 450055137.6 | 7.241725381 | 0.007915154 | | Residual | 153 | 9508567701 | 62147501.31 | | | | Total | 154 | 9958622839 | | | | | | | | | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Intercept | 9854.041192 | 2894.819474 | 3.404026151 | 0.000847889 | 4135.063875 | 15573.01851 | Weight | 2.843766419 | 1.056751555 | 2.691045407 | 0.007915154 | 0.756058281 | 4.931474557 |

Table 1 – Simple Linear Regression Model (Y and X)
Simple linear regression equation
Ŷi=b0+b1Xi
From Table 1, we can see that b0 = 9854.0412 and b1 = 2.8438
Ŷi=9854.0412+2.8438Xi

Figure 1 – Scatter Plot – Weight of Car vs Price of Car
(b) Interpret the slope b1 measures the estimated change in the average value of Y as a result of one-unit change in X. Thus, the slope value tells us that the price of a car increases by approximately $2.84, on average, for each additional pound increase in weight of a car.
(c) Interpolation
When Xi = 3000
Ŷi=9854.0412+2.8438×3000
Ŷi=$18385.34
(d) Coefficient of Determination
From Table 1 we can see that SSR = 450055137.6 and SST = 9958622839
Coefficient of Determination= r2=SSRSST

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