Y Values X Values 3.1 60 3.6 61 3.8 62 4 63 4.1 65 To the following questions, c
ID: 1180664 • Letter: Y
Question
Y Values
X Values
3.1
60
3.6
61
3.8
62
4
63
4.1
65
To the following questions, carry out answers to 3 decimal places if needed. Do not round answers up or down.
b=
a=
Y=
3. Calculate the standard error of estimate and the standard error of Coefficient
Standard error of estimate =
Standard error of Coefficient =
4. Make a prediction of Y when X = 64.
Prediction y=
5. Calculate a 95% prediction interval when X = 64.
Predicted value of y will lie between the (lower value) and (higher value)
6. Compute the coefficient of determination.
Coefficient of determination =
Y Values
X Values
3.1
60
3.6
61
3.8
62
4
63
4.1
65
Explanation / Answer
Correlation Co-efficient :
Correlation(r) =[ N?XY - (?X)(?Y) / Sqrt([N?X2 - (?X)2][N?Y2 - (?Y)2])]
where
N = Number of values or elements
X = First Score
Y = Second Score
?XY = Sum of the product of first and Second Scores
?X = Sum of First Scores
?Y = Sum of Second Scores
?X2 = Sum of square First Scores
?Y2 = Sum of square Second Scores
Correlation Co-efficient Example: To find the Correlation of
Step 1: Count the number of values.
N = 5
Step 2: Find XY, X2, Y2
See the below table
Step 3: Find ?X, ?Y, ?XY, ?X2, ?Y2.
?X = 311
?Y = 18.6
?XY = 1159.7
?X2 = 19359
?Y2 = 69.82
Step 4: Now, Substitute in the above formula given.
Correlation(r) =[ N?XY - (?X)(?Y) / Sqrt([N?X2 - (?X)2][N?Y2 - (?Y)2])]
= ((5)*(1159.7)-(311)*(18.6))/sqrt([(5)*(19359)-(311)2]*[(5)*(69.82)-(18.6)2])
= (5798.5 - 5784.6)/sqrt([96795 - 96721]*[349.1 - 345.96])
= 13.9/sqrt(74*3.14)
= 13.9/sqrt(232.36)
= 13.9/15.24336
= 0.9119
This example will guide you to find the relationship between two variables by calculating the Correlation Co-efficient from the above steps.
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