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...

 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.

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