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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
&#931;X=14 &#931;Y=21,000 &#931;X2=98 &#931;XY=147,000 &#931;Y2= 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 = &#931;X/3 = 14/3 = 4.67
Mean of Y = &#931;Y/3 = 21,000/3 = 7,000
b = &#931;XY - n(mean of X)(mean of Y)
&#931;X2 - 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.

\$2.19