In a simple linear regression problem, suppose that = 12.48 and = 124.8. Then the percentage of variation explained must be 0.90.

Question

In a simple linear regression problem, suppose that  = 12.48 and  = 124.8. Then the percentage of variation explained  must be 0.90.

Quizplus · Accepted Answer

The percentage of variation explained is calculated using the formula:
Percentage of variation explained = (SSR/SST) * 100
where, SSR = sum of squares due to regression
SST = total sum of squares
In this case, SSR = (β1*11eb06d9_cc89_937a_8177_8d291d4b4f10_TB1387_01 + β0 - mean of y)², 
and SST = (y - mean of y)²
Using the given values, we can find β1 and β0:
β1 = (11eb06d9_cc89_937d_8177_09ad9383420f_TB1387_11 - 11eb06d9_cc89_937b_8177_952894eee0a1_TB1387_00)/(11eb06d9_cc89_937c_8177_b948fac1ad32_TB1387_11 - 11eb06d9_cc89_937a_8177_8d291d4b4f10_TB1387_01) = 10
β0 = mean of y - β1*mean of x = 12.48 - 10*1.5 = -2.52

Substituting these values, we get:
SSR = (10*1.5 - 2.52 - 12.48/2)² + (10*3 - 2.52 - 124.8/2)² = 359.55
SST = (12.48 - 12.48/2)² + (124.8 - 124.8/2)² = 4180.62

Therefore, Percentage of variation explained = (359.55/4180.62) * 100 = 8.6%
Since this is less than 90%, the given statement is false. However, we can check that if 11eb06d9_cc89_937d_8177_09ad9383420f_TB1387_11 was actually equal to 125, then the percentage of variation explained would be 90%.

In a Simple Linear Regression Problem, Suppose That =