Q1. The following table represent a set of data on two variables Y and X. (a) Determine the linear regression equation Y = a + bX. Use your line to estimate Y when X = 15. (b) Calculate the Pearsonâ€™s correlation coefficient between the two variables. (c) Calculate Spearman's correlation Y 5 15 12 6 30 6 10 X 10 5 8 20 2 24 8?

Given the set of numbers Y = 5,15,12,6,30,6,10 and X = 10,5,8,20,2,24,8 the equation of a simple linear regression model becomes: Y = -0.77461X +20.52073.

When X is equal to 15, the equation predicts a Y value of 8.90158.

Next, to calculate the Pearson Correlation Coefficient, we use the equation r = (sum(x-xbar)(y-ybar))/(root(sum(x-xbar)^2 sum(y-ybar)^2)).

Next, inserting values, the equation becomes r = (-299)/(root((386)(458))) = -299/420.4617,

Therefore, Pearson's Correlation Coefficient is -0.71112

Finally, to calculate Spearman's Correlation, we use the following equation: p = 1 - [((6(sum(d^2))/(n(n^2-1))]

To use the equation we first rank the data, calculate the difference in rank as well as the squared difference in rank. The sample size, n, is 7 and the sum of the square of rank differences is 94

Solving p = 1 - ((6)(94))/(7(7^2-1) = 1 - (564)/(336) = 1 - 1.678571 = -0.67857

Therefore, Spearman's Correlation is -0.67857

Updated on August 5, 2018

By CWanamaker
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