1. Unit 3: Scatterplots and Linear Regression More Ways to Find the LSRL
3.2.4

2. Given a set of data, find the LSRL using technology
What we know
Given a set of data, find the LSRL using technology

3. Finding an LSRL: Computer Output
In many cases, the Least Squares Regression is already done on a computer. The results can be given in the form of a “computer output” chart.

4. Computer Output
Windmills generate electricity by transferring energy from wind to a turbine. A study was conducted to examine the relationship between wind velocity in miles per hour (mph) and electricity production in amperes for one particular windmill. For the windmill, measurements were taken on twenty-five randomly selected days, and the computer output for the regression analysis for predicting electricity production based on wind velocity is given below.

5. Computer Output
Windmills generate electricity by transferring energy from wind to a turbine. A study was conducted to examine the relationship between wind velocity in miles per hour (mph) and electricity production in amperes for one particular windmill. For the windmill, measurements were taken on twenty-five randomly selected days, and the computer output for the regression analysis for predicting electricity production based on wind velocity is given below.

6. Computer Output a b x-var
Windmills generate electricity by transferring energy from wind to a turbine. A study was conducted to examine the relationship between wind velocity in miles per hour (mph) and electricity production in amperes for one particular windmill. For the windmill, measurements were taken on twenty-five randomly selected days, and the computer output for the regression analysis for predicting electricity production based on wind velocity is given below. a
x-var b

7. Example #1
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below.
Write the equation for the fitted regression line.
Interpret the slope and y-intercept in context of the question

8. Example #1 Solution
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below. a) a b

9. Example #1 Solution
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below. a) a b
Little Credit!!

10. Example #1 Solution
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below. a)

11. Example #1 Solution
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below. a)

12. Example #1 Solution
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below. a)

13. Example #1 Solution
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below. a)
X-var

14. Example #1 Solution
A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she had allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output is shown below. a) b) Slope: On average, when the number of hours allocated to work increases by 1, the number of hours allocated to studying increases by about y-intercept: When the number of hours allocated to work is 0, the number of hours allocated to studying is about 8.107

15. Example #2
In a study of the performance of a computer printer, the size (in kilobytes) and the printing time (in seconds) for each of 22 small text files were recorded. A regression line was a satisfactory description of the relationship between size and printing time. The results of the regression analysis are shown below.
2002 released AP exam (multiple choice)
Write the equation for the fitted regression line.
Interpret the slope and y-intercept in context of the question

16. Example #2 Solution LSRL:
Slope: On average, as computer size increases by 1 kilobyte, the printing time increases by about seconds
y-int: When size is 0, the printing time is about seconds.

17. Finding LSRL: Summary Statistics
What if you are not given data AND you are not given the computer output?
Option 3…Use summary statistics and formulas.

18. Finding LSRL: Summary Statistics
Where
is the mean of the x-data
is the mean of the y-data
is the standard deviation of the x-data
is the standard deviation of the y-data
is the correlation coefficient of the x/y data

19. Good News!
y-intercept
slope

20. Example #3
A professor gave an end-of-course survey to her students that asked them to estimate the number of hours they devoted to the course per week and asked them to rate the course on a scale of 0 to 10 (where 0 represents not enjoying the course at all and 10 represents favorite course of all time). She wants to find the LSRL of rating of course on hours devoted to the course. The number of hours devoted to the course per week has a mean of 4.25 and a standard deviation of The course rating has a mean of 7.22 and a standard deviation of The professor found the correlation to be Find the equation of the LSRL of rating of course on hours devoted to the course.

21. Example #3 Solution
A professor gave an end-of-course survey to her students that asked them to estimate the number of hours they devoted to the course per week and asked them to rate the course on a scale of 0 to 10 (where 0 represents not enjoying the course at all and 10 represents favorite course of all time). She wants to find the LSRL of rating of course on hours devoted to the course. The number of hours devoted to the course per week has a mean of 4.25 and a standard deviation of The course rating has a mean of 7.22 and a standard deviation of The professor found the correlation to be Find the equation of the LSRL of rating of course on hours devoted to the course.

22. x = hours devoted to course
Example #3 Solution
A professor gave an end-of-course survey to her students that asked them to estimate the number of hours they devoted to the course per week and asked them to rate the course on a scale of 0 to 10 (where 0 represents not enjoying the course at all and 10 represents favorite course of all time). She wants to find the LSRL of rating of course on hours devoted to the course. The number of hours devoted to the course per week has a mean of 4.25 and a standard deviation of The professor found the correlation to be The course rating has a mean of 7.22 and a standard deviation of Find the equation of the LSRL of rating of course on hours devoted to the course.
x = hours devoted to course
y = rating of course

23. Example #3 Solution
A professor gave an end-of-course survey to her students that asked them to estimate the number of hours they devoted to the course per week and asked them to rate the course on a scale of 0 to 10 (where 0 represents not enjoying the course at all and 10 represents favorite course of all time). She wants to find the LSRL of rating of course on hours devoted to the course. The number of hours devoted to the course per week has a mean of 4.25 and a standard deviation of The course rating has a mean of 7.22 and a standard deviation of The professor found the correlation to be Find the equation of the LSRL of rating of course on hours devoted to the course.

24. Example #3 Solution
A professor gave an end-of-course survey to her students that asked them to estimate the number of hours they devoted to the course per week and asked them to rate the course on a scale of 0 to 10 (where 0 represents not enjoying the course at all and 10 represents favorite course of all time). She wants to find the LSRL of rating of course on hours devoted to the course. The number of hours devoted to the course per week has a mean of 4.25 and a standard deviation of The course rating has a mean of 7.22 and a standard deviation of The professor found the correlation to be Find the equation of the LSRL of rating of course on hours devoted to the course.

25. Example #3 Solution
A professor gave an end-of-course survey to her students that asked them to estimate the number of hours they devoted to the course per week and asked them to rate the course on a scale of 0 to 10 (where 0 represents not enjoying the course at all and 10 represents favorite course of all time). She wants to find the LSRL of rating of course on hours devoted to the course. The number of hours devoted to the course per week has a mean of 4.25 and a standard deviation of The course rating has a mean of 7.22 and a standard deviation of The professor found the correlation to be Find the equation of the LSRL of rating of course on hours devoted to the course.

26. Example #3 Solution

27. In Video Quiz
A set of data is collected where x = height of a 4th grader and y = length of jump. If the mean height of the 4th graders is 125 cm with a standard deviation of 10 cm and the mean length of jump is 38 inches with a standard deviation of 7 inches, find the LSRL of length of jump on height if the correlation is 0.75.

28. In Video Quiz Solution
A set of data is collected where x = height of a 4th grader and y = length of jump. If the mean height of the 4th graders is 125 cm with a standard deviation of 10 cm and the mean length of jump is 38 inches with a standard deviation of 7 inches, find the LSRL of length of jump on height if the correlation is 0.75.

29. Wrap Up After this lesson, you should be able to…
Find the LSRL given computer output
Find the LSRL using summary statistics and formulas (from the formula sheet)