# Linear Relations

Which relationships are linear?

a) Quantity Profit

0 $0

1 $1,500

4 $6,000

9 $13,500

b) Quantity Metal Used

0 0 oz

1 8 oz

2 18 oz

3 26 oz

c) Quantity Fixed Expenses

0 $3,000

1 $3,000

3 $3,000

5 $3,000

e) Quantity Metal Used

0 0 oz

1 8.5 oz

4 17 oz

9 25.5 oz

Which relationships are linear

a) y 3x-7 b) y=$4,000

Which relationships are perfectly linear and which are not:

Quantity Metal Used

7 17.5 oz

0 0 oz

9 23.5 oz

3 7.5 oz

Quantity Fixed Expenses

3 oz $4,200

0 oz $4,200

5 oz $4,200

1 oz $4,200

#### Solution Preview

Thanks for using BrainMass.com. Have a great day. Please see the attached file.

Linear relationship is a straight-line relationship between two variables such that the value of the dependent variable is a gradient times the independent variable plus a constant.

Linear Relationship =

Y = bX + a where b is the dependent variable while X is independent variable.

Which relationships are linear?

a) Quantity Profit

0 $0

1 $1,500

4 $6,000

9 $13,500

* I WILL CREATE REGRESSION ANALYSIS FOR A.

X is the number of quantity

Y is the total metal used

X Y X2 XY Y2

1 1,500 # 1 1,500 2,250,000

4 6,000 # 16 24,000 36,000,000

9 13,500 # 81 121,500 182,250,000

14 21,000 98 147,000 220,500,000

ΣX=14 ΣY=21,000 ΣX2=98 ΣXY=147,000 ΣY2= 220,500,000

Regression equation

Y = bX + a, Y is the total costs.

a is Y-axis intercept

b is the slope of the regression line

X is number of quantity

Mean of X = ΣX/3 = 14/3 = 4.67

Mean of Y = ΣY/3 = 21,000/3 = 7,000

b = ΣXY - n(mean of X)(mean of Y)

ΣX2 - n(mean of X)2

= 147,000 - 3(4.67)(7,000)

98 - 3(4.67)2

= 147,000 - 98,070

32.57

= ...

#### Solution Summary

This solution is comprised of solution in calculation to answer the request of the assignment in text file.