Question

7. A group of friends who graduated from college within the last couple of years really enjoyed statistics. To amuse themselves one Friday night, they decided to analyze the relationship between their incomes and the number of years since they graduated. They found the following data:

	Adam	Joe	Nick	Katie	Marie	Anne
Years since graduation	4	2	1	2	4	1
Salary / $1000	87	78	69	79	88	68

While these are not many data points, they nevertheless decided to do some regression analysis.

1. Find the linear least-squares regression line for this data.
2. Calculate the R² value (the coefficient of determination). What does this tell you?
3. Analyze the lack-of-fit and compute the relevant statistic for it. What does this tell you?
4. Taking these 6 friends as representative of all graduates (despite the small sample size), what does this linear regression model say about the expected salary after 8 years (give a single number, no interval needed)?
5. Do you think the answer in part d is reasonable or not? Explain why. Hint: it’s not about the small sample size or about your general expectations of salary after school.

Answer 1

A)The linear least squares regression line is given as predicted salary = 64 + 6.071(years)

B) Coefficient of determination,R² = 1-(SSR/TSS) = 0.948

A high value of R²implies that the model fits the data very well.

C)The F statistic is used to analyse the fit of the model .

Here the F value is 73.257 with p value as .001 which implies there is no lack of fit in the model and the model fits the data well

The slope coefficient is also significant since the p value for slope efficient is .001 with t value as 8.559

D)The predicted salary for 8 years after graduation is 64+6.071(8) = 112.57 = 113(app)

E)The answer in part D is not reasonable because for this problem the predictive interval at 5℅ level of significance is (70,88) but our value (112) is out of scope of the model