2. The mathematics department of a large state university would like to use the

Question

2. The mathematics department of a large state university would like to use the number of freshmen entering the university x to predict the number of students y who will sign up for freshman-level math courses in the fall semester. Here are data for recent years. The regression line is y -1.25x +1690 with correlation 0.896 4500 4800 4400 4300 4000 4300 4300 4400 y 7400 7600 7100 6900 6600 7200 7200 7400 a) Predict the number of students to sign up for freshman math if the number of entering freshmen is 4400. b) What percent of the observed variations in the number of students who sign up for freshman-level math courses in the fall semester can be explained by the linear relationship between the number of freshmen entering and the number signing up for math courses? c) Is the relationship positive or negative?

Explanation / Answer

a)

if x = 4400, then Y = 1.25*4400 + 1690 = 7190

b) Required percentage of variation = 100 * (0.896)2 = 80.28%

c) Here slope = 1.25 which is positive

then correlation is also positive

So there is positive relation

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