Question

The following data give the number of hours 5 students spent studying and their corresponding grades on their exams. Hours Studying 4 5 5 5 5 Grades 63 67 77 95 100 Step 1 of 5 : Calculate the sum of squared errors (SSE). Use the values b0=−24.0000 and b1=21.7500 for the calculations. Round your answer to three decimal places.

Answer 1

Solution

Back-up Theory

The linear regression model: Y = β₀ + β₁X + ε, ………………..………………………..(1)

Sum of squared errors (SSE) = Syy – b12.Sxx ..........................................................(2)

Where

Mean X = Xbar = (1/n) Σ(i = 1 to n)x_i ………………………………………….……….….(3)

Mean Y = Ybar = (1/n) Σ(i = 1 to n)y_i ………………………………………….……….….(4)

Sxx = Σ(i = 1 to n)(x_i – Xbar)² ………………………………………………..…………....(5)

Syy = Σ(i = 1 to n)(y_i – Ybar)² ……………………………………………..…….…………(6)

Now to work out the solution,

Let x = hours of study and y = grade

n	5
Xbar	4.80
ybar	80.40
Sxx	0.80
Syy	1091.20
b1	21.75
SSE	712.750

So, SSE = 712.750 Answer

DONE