Solve the following CORRELATION and REGRESSION question and please show your calculations, and explain your findings.

Question

The following data relates to marks obtained by students in two Continuous Assessment Tests Use the information to answer the questions that follow:

CAT 1: 65 48 15 28 41 59 41 10 24 56

CAT 2: 28 33 20 23 69 45 53 15 35 57

1. Calculate the Spear-man's and Karl Pearson’s correlation coefficients and give their interpretations
2. Calculate the Coefficient of Determination and interpret it.
3. Compute the Regression of CAT 2 marks on CAT 1 and use it to predict the marks that a student who got 60 in CAT 1 is likely to get in CAT 2.

Answer 1

Spearman's is 0.50456. <--- not good

Peason's is 0.5186. <--- not good

closer to 1 or -1, the better; The linear model is NOT a good fit for the data

Coefficient of Determination is 26.9%

only 26.9% of the dependent var can be explained. the rest is error

ŷ = 0.48456X + 19.04745

For x = 60, y = 0.48456*60+19.04745 = 48.12105