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
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