2.76 College students by state. Refer to Exercise 2.21 (page 99, where you exami
ID: 3258078 • Letter: 2
Question
2.76 College students by state. Refer to Exercise 2.21 (page 99, where you examined the relationship between the number of undergraduate college students and the populations for the 50 states. Figure 2.22 gives the output from a software package for the regression. Use this out put to answer the following questions L, COLLEGE (a) What is the equation of the least-squares regression line? (b) What is the value of r (c) Interpret the value of r2. (d) Does the software output tell you that the relation- ship is linear and not, for example, curved? Explain your answer.Explanation / Answer
From figure 2.21,
(a) the regression equation is,
y = -15044.917 + 0.053 * x,
where y denotes the dependent variable i.e. Undergrads and x denotes the independent variable i.e. Population.
(b) The value of R-square is 0.968.
(c) R-square value 0.968 implies that 96.8% of total variation in y (Undergrads) is explained by x (Population).
(d) Since R-square is close to 1 and it measures the strangth of linear relationship, i.e. the relationship is strong if R-square is close to 1. So here linear relationship holds true.
From figure 2.22,
(a) the regression equation is,
y = 8491.907 + 0.048 * x,
where y denotes the dependent variable i.e. Undergrads and x denotes the independent variable i.e. Population.
(b) The value of R-square is 0.942.
(c) R-square value 0.942 implies that 94.2% of total variation in y (Undergrads) is explained by x (Population).
(d) Since R-square is close to 1 and it measures the strangth of linear relationship, i.e. the relationship is strong if R-square is close to 1. So here linear relationship holds true.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.