Question

Queshon 3 of 3 Question 3 10 points Save Answer Question Code 3A46 We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its five-year performance Sa mutual funds were selected at random, and their assets and rates of return are shown below X values (31 8, 14.4, 278, 13.7.27 3. 15.1) (in Smillions) Y values (105, 6.6, 10.9, 8.8, 10.7.5.6) (in %) a) Plot the Scatter Plot on the written work sheet b) Find the equation of the regression line (Round to 4 decimal places) y a c) Find the correlation coefficient (Round to 4 decimal places) = 160W ENG 06:53 29-07-2020 w o 5

Answer 1

solution:

scatter plot

Y Values X Values

after calculating

Sum of X = 130.1
Sum of Y = 53.1
Mean X = 21.6833
Mean Y = 8.85
Sum of squares (SS_X) = 331.4283
Sum of products (SP) = 77.805

Regression Equation = ŷ = bX + a

b = SP/SS_X = 77.81/331.43 = 0.23476

a = M_Y - bM_X = 8.85 - (0.23*21.68) = 3.75969
the linear regression is ŷ = 0.23476X + 3.75969

b) coefficient of correlation :

X Values
∑ = 130.1
Mean = 21.683
∑(X - M_x)² = SS_x = 331.428

Y Values
∑ = 53.1
Mean = 8.85
∑(Y - M_y)² = SS_y = 25.975

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 77.805

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 77.805 / √((331.428)(25.975)) = 0.8386
The coefficient of correlation is
r= 0.8386