The following equation describes the relationship between fourth-grade pass rate

Question

The following equation describes the relationship between fourth-grade pass rates on a math test, measured as a percent, spending per student (expr. in dollars), and he percentage of students eligible for free and reduced-price lunches (lunch): math 4 = beta_0 + beta_1 log (expr) + beta_2 lunch + u Argue that beta_1/100 is the (ceteris paribus) percentage point change in math 4 when expr increase by 10 percent. If expenditure per student is higher at poor schools, are log log (expr) and lunch positively or negatively correlated? Using the data, the following equations are estimated: math 4 = 84.84 - 1.52 log (expr), n = 1, 823, R^2 = .0003. math 4 = beta_0 + 11.38 log (expr) - .471 lunch, n = 1, 823, R^2 = 370. From the simple and multiple regression results, determine whether, in this sample. log (expr) and lunch are positively or negatively correlated.

Explanation / Answer

(1) so if there is 10% increase in exppp

so change in math4 = 1 log ( 1.1 * exppp) - 1 log (exppp) = 1 log ( 1.1) = 0.011 = 1/100

(2) If math4 result is remain constant then it is said that expenditure per student or exppp is higher in poor schools which means it will have more student who will have free lunches at school so in this case log log ( expppp) and lunch will be positively related.

(3) The simple logarithamic regression shows negative relation in between math4 and log(exppp) but it is a veru weak corelation coefficient of 0.0003. but from multiple regression we can see that log (exppp) and lunch are in different direction so it can be said that both are negatively related.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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