Question 2 The following data shows the yearly income (in $1000) and age of a sa

Question

Question 2 The following data shows the yearly income (in $1000) and age of a sample of seven individuals Y-Income (in $1000 - Age 20 24 24 25 26 27 34 18 20 23 34 24 27 27 Where = 180 = 173 XY = 4513 2-4443 2-4738 a. Develop the estimates of simple regression equation, that is? a + bx b. Interpret the intercept of the regression. c. Interpret the slope of the regression d Estimaic the yearlyncme ofa 30 year-old indvidual. Give yourla Compute the correlation coefficient. Use your answer in (e) above to compute the coefficient of determination. Interpret the coefficient of determination e. f. Question 3

Explanation / Answer

Question 2

Part a

Formula for regression coefficients are given as below:

b = (XY – n*Xbar*Ybar)/(X^2 – n*Xbar^2)

a = Ybar – b*Xbar

By using given values, we have

b = (4513 – 7* 25.71429*24.71428571)/(4443 – 7*25.71429^2)

b = 0.384812287

a = Ybar – b*Xbar

a =24.71428571 – 0.384812287*Xbar

a = 16.20392491

Regression equation is given as below:

Y = 16.20392491 + 0.384812287*X

Income (in $1000) = 16.20392491 + 0.384812287*Age

Part b

For this regression model, the value for intercept is given as 16.20392491, which means the value of income would be 16.20392491 when there is absent of age.

Part c

Slope for the given regression model is given as 0.384812287, which indicate the increment in income when there is a unit increase in age.

Part d

Here, we have to predict the value of income when age = 30 years

Income (in $1000) = 16.20392491 + 0.384812287*Age

Income (in $1000) = 16.20392491 + 0.384812287*30

Income (in $1000) = 27.74829

Income = $27748.29

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.