Linear Relations
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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
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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
= ...
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