Chapter 4, Problem 32P

A

Summary Introduction

Interpretation: Construct a regression formula for anticipating the overhead expense using linear regression, based on the project duration.

Concept Introduction: The method followed in predicting the future value depending on the previous forecast including the portion of errors in the previous forecast is called Simple Exponential Smoothing forecast.

Answer to Problem 32P

The required regression equation for predicting overhead expense is Y=5399.22+29.7217x.

Explanation of Solution

Given Information:

  

Project Code	Project Duration (days) (X)	Overhead Expense (Y)	XY	X2
A11	72	$5,900	$424,800	5184
A12	158	$10,303	$1,627,874	24964
A14	124	$9,054	$1,122,696	15376
A18	96	$6,644	$637,824	9216
A22	152	$10,718	$1,629,136	23104
B2	174	$10,332	$1,797,768	30276
B33	124	$8,804	$1,091,696	15376
B23	105	$8,884	$932,820	11025
B10	63	$7,916	$498,708	3969
B14	58	$8,267	$479,486	3364
B7	83	$8,503	$705,749	6889
	109.9090909	8665.9091	10948557	148743
	12080.00826
b				29.7217
a				5399.22

Thus, the regression equation with the derived values will be,

  $\begin{array}{l}Y=a+bx\\ Y=5399.22+29.7217x\end{array}$

B

Summary Introduction

Interpretation: Find out the coefficient of determination for the given projects.

Concept Introduction: The proportion of variance occurring in the dependent variable forecasted based on the independent variable is called the Coefficient of Determination.

Answer to Problem 32P

The coefficient of determination, r² is 0.6264.

Explanation of Solution

Given Information:

  $Y=5399.22+29.7217x$

Project Code	Project Duration (days) (X)	Overhead Expense (Y)
A11	72	$5,900
A12	158	$10,303
A14	124	$9,054
A18	96	$6,644
A22	152	$10,718
B2	174	$10,332
B33	124	$8,804
B23	105	$8,884
B10	63	$7,916
B14	58	$8,267
B7	83	$8,503
r2		0.6264

Thus, coefficient of determination is 0.6264.

C

Summary Introduction

Interpretation: Determine what the forecast of the overhead expense suggests for the project of 110 days long.

Concept Introduction: Using regression, we will be able to define relationship between any two variables, denoting the cause and effect. The method can also be used to forecast the future depending on the past performances.

Answer to Problem 32P

The forecasted expense of overhead for 110 days long project is $8,668.61.

Explanation of Solution

Given Information:

The project is 110 days long.

  $\begin{array}{l}Y=5399.22+29.7217x\\ Y=5399.22+29.7217(110)\\ Y=5399.22+3269.387\\ Y=\$8668.61\end{array}$

Thus, the forecasted overhead expense is $8,668.61.

D

Summary Introduction

Interpretation: With the information, build a better way in using linear regression for forecasting overhead expense.

Concept Introduction: Using regression, we will be able to define relationship between any two variables, denoting the cause and effect. The method can also be used to forecast the future depending on the past performances.

Answer to Problem 32P

The forecasted overhead expense is $8946.64.

Explanation of Solution

Given Information:

The given value of ‘a’ is 1542.02 and the given value of ‘b’ is 57.99.

Project Code	Project Duration (days) (X)	Overhead Expense (Y)	XY	X2
A11	72	$5,900	$424,800	5184
A12	158	$10,303	$1,627,874	24964
A14	124	$9,054	$1,122,696	15376
A18	96	$6,644	$637,824	9216
A22	152	$10,718	$1,629,136	23104
	120.4	$8,524	5442330	77844
	14496.2
b				57.99
a				1542.02
r2				0.9655

Thus, with the above derived values of ‘a’ and ‘b’, the linear regression model would be:

  $\begin{array}{l}Y=a+bx\\ Y=1542.02+57.99x\end{array}$

  

  

  $\begin{array}{l}Y=a+bx\\ Y=6928.14+18.35x\end{array}$

Now, substituting the values in the previous linear regression equation:

  $\begin{array}{l}Y=a+bx\\ Y=1542.02+57.99(110)\\ Y=1542.02+6378.9\\ Y=7920.92\end{array}$

For 110 days, the forecasted overhead expense is $7920.92.

Now, substituting the values in the later linear regression equation:

  $\begin{array}{l}Y=a+bx\\ Y=6928.14+18.35x\\ Y=6928.14+18.35(110)\\ Y=6928.14+2018.5\\ Y=8946.64\end{array}$

Thus, the forecasted overhead expense is $8946.64.