2. The mean income in a certain community $43,500 per year per adult community m

Question

2. The mean income in a certain community $43,500 per year per adult community member give-or-take S5,000. The mean number of years of education per adult community member is 14 years with a reported standard deviation of 1.5 years. The correlation coefficient r for these results is 0.61 a. Write the equation of the least squares regression line for this data using years of education as the explanatory variable. b. Estimate the income of an individual with 15 years of education. c. Interpret r2 in this context. d. A residual of 533.33 is associated with an individual with 13 years of education. Find the actual income this individual earns.

Explanation / Answer

a) here estimated slope b1 =r*Sy/Sx =0.61*5000/1.5=2033.333

and intercept bo =(Ybar-b1*Xbar) =43500-2033.333*14=15033.34

hence least square equation :Yhat =15033.34+2033.333*x

b) for x =15 ; estimated income=15033.34+2033.333*15 =45333.34

c)

r2 =0.612 =0.3721

which tells that 37.21% variation in predicted income through this model can be explained by variability in independent variable.

d)

for 13 year ; predicted income =15033.34+2033.333*13 =41466.67

therefore actual income =predicted +residual =41466.67+533.33=42000

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

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