Answer to Question #162632 in Statistics and Probability for Sunny

Question

Aptitude Test No. of claims settled in a month

65 68

70 60

60 62

77 80

75 85

50 40

53 52

73 62

65 60

82 81

Using regression analysis on the above data answer the following question:

A) if a new employee Sarah scores 88 on the test how many claims is she like to settle?

B) Interpret the coefficient of determination

Answer 1

Answer

The mean is given by

$\bar{x}$= $1 \over n$$Σx$

Applied test

$\bar{x}$ = 67

Claims

$\bar{y}$= 65

The slope is given by

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

β₁= $1149 \over 976$= 1.17725

The intercept is given by

 β₀= $\bar{y}$ - β₁$\bar{x}$

β₀= 65-67x 1.17725 = -13.876

The regression line is given by

y=-13.876+ 1.17725

a)

Excel formula

The output is given below

From the output, the regression equation is 

No. of claims settled in a month =-13.879 + 1.177254 (Aptitude Test)

To find the number of settlements substitute Aptitude Test = 88 in the regression equation.

The regression equation is 

No. of claims settled in a month =-13.879 + 1.177254 (Aptitude Test)

substitute Aptitude Test = 88

No. of claims settled in a month =-13.879 + 1.177254 (88)

=89.72

No. of claims settled in a month =90 (approximately)

Thus, the number of claims is she like to settle is 90.

b)

Error sum of square is given by

ESS = $Σ (y-\bar{y})^2$ = 399.335

Total sum of square is given by

TSS= $Σ (y-\bar{y})^2$ = 1752

The coefficient of determination is given by

R²=1-$ESS \over TSS$

R²=1-$399.335 \over 1752$

It shows that around 77.21% variation in the number of claims settled is explained by the aptitude test scores.