Question

x	y
74.5	45.7
68.9	67.9
81.8	45.1
61.6	57.7
57.7	69.1
97.7	32
80.6	70.5
81.9	51.1
90.8	31.3
69.5	51.4
60.1	64.8
69.3	52.7

1) Find the correlation coefficient and round it to three places.

2) Based on the data, calculate the regression line and give it in the form y=mx+b. Round each value of m and b to three decimal places.

3) Predict what value (on average) for the response variable will be obtained from a value of 63.7 as the explanatory variable. Do not use StatCrunch. Instead, use your equation from #2 and algebra to find your prediction. Show your work/calculations and round to 3 decimal places. Express your answer in a complete sentence form.

Answer 1

ΣX = 894.4
ΣY = 639.3
ΣX * Y = 46268.25
ΣX2 = 68351.2
ΣY2 = 36040.45

Part a)

r = -0.755

Part b)

Equation of regression line is Ŷ = a + bX


b = -0.818
a =( Σ Y - ( b * Σ X) ) / n
a =( 639.3 - ( -0.8178 * 894.4 ) ) / 12
a = 114.228
Equation of regression line becomes Ŷ = 114.228 - 0.818 X

Part c)

When X = 63.7
Ŷ = 114.228 + -0.818 X
Ŷ = 114.228 + ( -0.818 * 63.7 )
Ŷ = 62.121