Calculate Correlation Coefficients

1、s.id.8: calculate correlation coefficientss.id.8: calculate correlation coefficients interpret linear models8. compute (using technology) and interpret the correlation coefficient of a linear fit.overview of lesson- activate prior knowledge- present vocabulary and/or big ideas associated with the le

2、sson- connect assessment practices with curriculum- model an assessment problem and solution strategy- facilitate guided practice of student activity- facilitate a summary and share out of student workoptional: provide additional problem setsoptional hw - write the math assignment.vocabularycorrelat

3、ion a statistical measure that quantifies how pairs of variables are related; a linear relationship between two variables.correlation coefficient a number between -1 and 1 that indicates the strength and direction of the linear relationship between two sets of numbers. the letter “r” is used to repr

4、esent correlation coefficients. in all cases, .interpreting a correlation coefficient - what it meansevery correlation coefficient has two pieces of information:1. the sign of the correlation. a correlation is either positive or negative. a. with positive correlations, the variables increase or decr

5、ease together. b. with negative correlations, one variable increases while the other decreases.2. the absolute value of the correlation. a. the closer the absolute value of the correlation is to 1, the stronger the correlation between the variables. b. the closer the absolute value of the correlatio

6、n is to zero, the weaker the correlation between the variables.the sign of the correlation tells you what the graph will look like and negative correlationin general, one set of data decreases as the other set increases. an example of a negative correlation between two variables would be the relatio

7、nship between absentiism from school and class grades. as one variable increases, the other would be expected to decrease.no correlation sometimes data sets are not related and there is no general trend.a correlation of zero does not always mean that there is no relationship between the variables. i

8、t could mean that the relationship is not linear. for example, the correlation between points on a circle or a regular polygon would be zero or very close to zero, but the points are very predictably related.positive correlationin general, both sets of data increase together.an example of a positive

9、 correlation between two variables would be the relationship between studying for an examination and class grades. as one variable increases, the other would also be expected to increase.the absolute value of the correlation tells you the strength of the correlation.in a perfect correlation, when ,

10、all data points balance the equations and also lie on the graph of the equation.how to calculate a correlation coefficient using a graphing calculator: step 1. press . step 2. enter bivariate data in the l1 and l2 columns. all the x-values go into l1 column and all the y values go into l2 column. st

11、ep 3. turn the diagnostics on by pressing and scrolling down to . then, press . the screen should respond with the message . note: if diagnostics are turned off, the correlation coefficient will not appear beneath the regression equation.step 4. use and the appropriate type of regression, then step

12、5. the r value that appears at the bottom of the screen is the correlation coefficient. regents problems_1.what is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth?a.1.00c.b.0.93d.2.a nutritionist collected information about different brands of beef hot

13、 dogs. she made a table showing the number of calories and the amount of sodium in each hot dog.a) write the correlation coefficient for the line of best fit. round your answer to the nearest hundredth.b) explain what the correlation coefficient suggests in the context of this problem.s.id.8: calcul

14、ate correlation coefficientsanswer section1.ans:cstrategy #1: this problem can be answered by looking at the scatterplot. the slope of the data cloud is negative, so answer choices a and b can be eliminated because both are positive.the data cloud suggests a linear relationship, put the dots are not

15、 in a perfect line. a perfect correlation of would show all the dots in a perfect line. therefore, we can eliminate asnswer choice d.the correct answer is choice c. dims: does it make sense? yes. the data cloud shows a negative correlation that is strong, but not perfect. choice c is the best answer

16、.strategy #2: input the data from the chart in a graphing calculator and calculate the correlation coefficient using linear regression and the diagnostics on feature.step 1. create a table of values from the graphing view of the function and input it into the graphing calculator. xy18283543546181ste

17、p 2. turn diagnostics on using the catalog.step 3. determine which regression strategy will best fit the data. the graph looks like the graph of an linear function, so choose linear regression. step 4. execute the appropriate regression strategy with diagnositcs on in the graphing calculator.round t

18、he correlation coefficient to the nearest hundredth: step 4. select answer choice c. dims: does it make sense? yes. the data cloud shows a negative correlation that is strong, but not perfect. choice c is the best answer.pts:2ref:061411a1nat:s.id.8top:correlation coefficient and residuals2.ans:. the

19、 correlation coefficient suggests that as calories increase, so does sodium.strategy: use data from the table and a graphing calculator to find both the regression equation and its correlation coefficient.step 1. input the data from the table in a graphing calculator and look at the data cloud.step

20、2. turn diagnostics on using the catalog.step 3. determine which regression strategy will best fit the data. the graph looks like the graph of an linear function, so choose linear regression. step 4. execute the appropriate regression strategy with diagnositcs on in the graphing calculator.round the

21、 correlation coefficient to the nearest hundredth: dims: does it make sense? yes. the data cloud and the table show a positive correlation that is strong, but not perfect. a correlation coefficient of .94 is positive, but not a perfectly straight line.pts:4ref:011535a1nat:s.id.8top:correlation coeff

22、icient and residualsstandard “writing the math” assignmentstartwrite your name, date, topic of lesson, and class on your paper.part 1. copy the problem from the lesson and underline/highlight key words.part 2.state your understanding of what the problem is asking.part 3.answer the problem.part 4. ex

23、planation of strategy.part 5.create a new problem that addresses the same mathematical understandings.part 6.state the answer to your new problem.clearly label each of the six parts.grading rubriceach homework writing assignment is graded using a four-point rubric, as follows:part 1. statement of th

24、e problem. point is awarded for correctly restating the original problem. part 2. statement of what the problem is really asking. point is awarded for correctly identifying what the problem is asking you to find or do.part 3. solution to the problem. point is awarded for a correct solution to the pr

25、oblem.part 4. written analysis of the mathematics and solution strategy involved in the problem.up to 1 point is awarded for an explanation of the mathematics and solution strategy involved in the problem.part 5. an alternative version of the problem.up to 1 point is awarded for creating a new probl

26、em that involves similar mathematics and a similar solution strategy. part 6. solution to the alternative version of the problem. point is awarded for correctly solving the new problem that you have created.this assignment/activity is designed to incorporate elements of polyas four step universal al

27、gorithm for problem solving with the idea that writing is thinking. rationale for assignmenteach new york regents algebra i (common core) examination contains 13 open response problems. an analysis of the first three algebra i examinations revealed that approximately 51% (20 out of 39) of these open

28、 response problems instructed students to: 1) describe; 2) state; 2) explain; 3) justify or otherwise write about their answers. it is theorized that students can benefit from explicit instruction and writing routines that are applicable to solving these problems. exemplar of a writing the math assi

29、gnmentstudents nametopic:date: class: part 1. the problemtop electronics is a small business with five employees. the mean (average) weekly salary for the five employees is $360. if the weekly salaries of four of the employees are $340, $340, $345, and $425, what is the salary of the fifth employee?part 2. what is the problem asking?find the salary of the fifth employee.part 3. answerthe salary of the fifth employee is $350 per week.part 4. explanation of strategy the arithmetic mean or average c