Step 1: Researchers conducted a study on each state’s SAT Mathematics score and

Question

Step 1:
Researchers conducted a study on each state’s SAT Mathematics score and the proportion of that state’s high school seniors who took the SAT test. The SAT score is the response variable, and the proportion of that state’s high school seniors who took the SAT test is the explanatory variable

The least-squares regression line for predicting SAT Mathematics score from the proportion of seniors who took the SAT test is:
average Math SAT score = 588.4 - (1.228 x percentage taking)

Identify the statement that correctly interprets the meaning of slope b = -1.228, with reference to the relationship between these variables.

a) If the proportion of seniors taking the test increases by 1 percentage point, we expect the mean Mathematics SAT score to increase by 1.228 points.

b) If the proportion of seniors taking the test increases by 1 percentage point, we expect the mean Mathematics SAT score to decrease by 1.228 points.

c) If the proportion of seniors taking the test decreases by 1.228 percentage points, we expect the mean Mathematics SAT score to increase by 1 point.

Step 2:
Fill in the blank:

In the New York state, the percentage of high school seniors who took the SAT was 76%. The average Mathematics SAT score for the New York state is ___. (Give your answer to one decimal place.)

Step 1:
Researchers conducted a study on each state’s SAT Mathematics score and the proportion of that state’s high school seniors who took the SAT test. The SAT score is the response variable, and the proportion of that state’s high school seniors who took the SAT test is the explanatory variable

The least-squares regression line for predicting SAT Mathematics score from the proportion of seniors who took the SAT test is:
average Math SAT score = 588.4 - (1.228 x percentage taking)

Identify the statement that correctly interprets the meaning of slope b = -1.228, with reference to the relationship between these variables.

a) If the proportion of seniors taking the test increases by 1 percentage point, we expect the mean Mathematics SAT score to increase by 1.228 points.

b) If the proportion of seniors taking the test increases by 1 percentage point, we expect the mean Mathematics SAT score to decrease by 1.228 points.

c) If the proportion of seniors taking the test decreases by 1.228 percentage points, we expect the mean Mathematics SAT score to increase by 1 point.

Step 2:
Fill in the blank:

In the New York state, the percentage of high school seniors who took the SAT was 76%. The average Mathematics SAT score for the New York state is ___. (Give your answer to one decimal place.)

Explanation / Answer

Step 1

option b is correct.

Explanation:

when we have any regression line given in the linear form y=a+bx,

where: a and b are the constants,

x is the explanatory variable (in this case proportion of the student )and

y is the response variabe(in this case the average SAT score)

then it means that y is proportionately increasing with x. that is to say if we increase x by 1 point then y will increase by b points. However what we need to understand here is the significance of the negative sign in the expression (y=a-bx). in this case only change in the meaning is that y is now inversely proportional to x that is to say if x increases by 1 point then y decreases by b points.

hence comparing this equation with the given one in the question, we find that statement b is the only correct statement.

Step 2

to solve this we just need to use the eqation given in the question.

Mathematics SAT score for the New York state = 588.4 - (1.228 x76) =495.1

Thank you. Hope it helps.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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