Answer to Question #162734 in Quantitative Methods for Sunny

Question

It was proposed that a study be conducted on the number of start- ups and annual number of business bankruptcies. Data collected was six year period. Develop regression equation and forecast the bankruptcy numbers given the start ups for the forthcoming year to be 60. Interpret the significance of predictor through R Square

Business Bankruptcies Start ups

(in 1000)

34.3 58.1

35 55.4

38.5 57

40.1 58.5

35.5 57.4

37.9 58

Answer 1

Answer

Working

Regression Line

The mean is given by

$\bar{x}$= $1 \over n$$Σx$

bankruptcies

$\bar{x}$ = $344.4 \over 6$ = 57.4

Startups

$\bar{y}$= $221.3 \over 6$ =36.8833

The slope is given by

β₁= $Σ (x-\bar{x}) (y-\bar{y}) \over Σ (x-\bar{x})^2$

β₁= $5.46 \over 6.22$= 0.8778

The intercept is given by

 β₀= $\bar{y}$ - β₁$\bar{x}$

β₀= 36.8833-57.4 x 0.8778 = -13.5032

The regression line is given by

y=-13.5032+ 1.17725x

When start ups = 60, then predicted bankruptcies are

y = -13.5032 + 0.8778 x 60

y = 39.1656

Error sum of square is given by

ESS = $Σ (Residual)^2$ = 21.3355

Total sum of square is given by

TSS= $Σ (y-\bar{y})^2$ = 26.1283

The r-square is given by

R²=1-$ESS \over TSS$

R²=1-$21.3355 \over 26.1283$

R²= 0.1834

Interpretation

It shows that around 18.34% variation in the bankruptcies is explained by the number of start-ups.