In Question, use linear regression to find the requested linear model.
The table shows, for selected states, the percent of high school students in the class of 2005 who took the SAT and the average SAT math score.*
State | Students Who Took SAT (%) | Average Math Score |
Connecticut | 86 | 517 |
Delaware | 74 | 502 |
Georgia | 75 | 496 |
Idaho | 21 | 542 |
Indiana | 66 | 508 |
Iowa | 5 | 608 |
Montana | 31 | 540 |
Nevada | 39 | 513 |
New Mexico | 13 | 547 |
North Dakota | 4 | 605 |
Ohio | 29 | 543 |
Pennsylvania | 75 | 503 |
South Carolina | 64 | 499 |
Washington | 55 | 534 |
(a) Make a scatter plot of average SAT math score y and percent x of students who took the SAT, with the data points arranged in order of increasing values of x.
(b) Find a linear model for the data.
(c) What is the slope of your linear model? What does this mean in the context of the problem?
(d) Here are the data on four additional states. How well does the model match the actual figures for these states?
State
Students Who Took SAT (%)
Average Math Score
Alaska
52
519
Arizona
33
530
Hawaii
61
516
Oklahoma
7
563
*The College Board.
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