REGRESSION ANALYSIS

Identify the independent and dependent variable;
Draw the best fit line on a scatter plot;
Calculate the slope and the y-intercept of the regression line;
Interpret the calculated slope and the y-intercept of the regression line;
Predict the value of the dependent variable given the value of the independent variable; and
Solve problems involving regression analysis.

Visit the Website for more Services it can offer:
https://cristinamontenegro92.wixsite.com/onevs

1. REGRESSION ANALYSIS

2. Learning Competencies The learner will be able to: Identify the independent and dependent variable; Draw the best fit line on a scatter plot; Calculate the slope and the y-intercept of the regression line; Interpret the calculated slope and the y-intercept of the regression line; Predict the value of the dependent variable given the value of the independent variable; and Solve problems involving regression analysis.

3. Independent variable Dependent variable The straight line that best illustrates the trend or direction that the data points seem to follow is called the best-fit line or line of the best fit . Steps: Draw the line Calculate slope and y-intercept Find the equation of the line Bivariate data in Scatter plot

4. Consider the following data. Construct a scatter plot. Draw the line of best fit. Calculate the slope and the y-intercept and then write the equation of the line of best fit. Solution Example 1 x 1 2 3 4 5 6 7 y 4 3 8 6 12 10 8

5. c. Step 1. Find the slope. Use the points (1,4) and (6,10) which are on the line. Step 2. Find the y-intercept. Use the slope-intercept form of the equation of a line and the point (1,4).  

6. Step 3. Write the equation of the line of best fit. Substitute the value of m and the value of b in . The equation of the line best fit is or if the slope and the y-intercept are rounded to nearest integer.  

7. However, if another student will use two points other than those used in the above computations, he would obtain a different equation for the line of best fit. The above computation is preferred if there is a perfect correlation between variables, or the points lie on a straight line. However, if the points are scattered or not on a straight line, there is a better way to find the equation of the line of best fit. This equation is called the equation of the regression line or simply regression equation .

8. The equation of the regression line is where y-intercept of the regression line; and slope of the regression line. The y-intercept formula : The slope formula :   Equation of Regression Line

9. Consider the following data: Find the equation of the regression line. Draw the graph of the regression equation on a scatter plot Solution Example 2 x 1 2 3 4 5 6 7 y 4 3 8 6 12 10 8 x y xy 1 4 4 1 2 3 6 4 3 8 24 9 4 6 24 16 5 12 60 25 6 10 60 36 7 8 56 49 x y xy 1 4 4 1 2 3 6 4 3 8 24 9 4 6 24 16 5 12 60 25 6 10 60 36 7 8 56 49

10. The equation of the regression line is   Solving and  

11. Scatter plot

12. Find the regression equation using the following data: Solution Example 3 x 5 10 20 8 15 25 y 40 26 18 30 20 15 x y xy 5 40 200 25 10 26 260 100 20 18 360 400 8 30 240 64 15 20 300 225 25 15 375 625 x y xy 5 40 200 25 10 26 260 100 20 18 360 400 8 30 240 64 15 20 300 225 25 15 375 625

13. The equation of the regression line is   Solving and  

14. Scatter plot

15. Shown below are the ages (x) and the systolic blood pressure numbers (y) of 9 male patients in a certain hospital. Find the regression equation. Solution Example 4 Age (x) 26 40 35 50 45 55 28 30 52 Systolic Blood pressure number 110 140 120 145 130 150 150 125 142

16. solution Patient x y xy 1 26 110 2860 676 2 40 140 5600 1600 3 35 120 4200 1225 4 50 145 7250 2500 5 45 130 5850 2025 6 55 150 8250 3025 7 28 150 4200 784 8 30 125 3750 900 9 52 142 7384 2704 Patient x y xy 1 26 110 2860 676 2 40 140 5600 1600 3 35 120 4200 1225 4 50 145 7250 2500 5 45 130 5850 2025 6 55 150 8250 3025 7 28 150 4200 784 8 30 125 3750 900 9 52 142 7384 2704

17. The equation of the regression line is   Solving and  

18. Scatter plot

19. Prediction and Estimation Using the Regression Equation for

20. The regression equation can be used to predict or estimate the value of the dependent variable if the value of the independent variable is given.

21. Consider the following data: Find the equation of the regression line. Draw the graph of the regression equation on the scatter plot. Estimate the value of if   Example 5 x 1 2 3 4 5 6 7 y 4 5 1 6 7 10 7

22. solution x y xy 1 4 4 1 2 5 10 4 3 1 3 9 4 6 24 16 5 7 35 25 6 10 60 36 7 7 49 49 x y xy 1 4 4 1 2 5 10 4 3 1 3 9 4 6 24 16 5 7 35 25 6 10 60 36 7 7 49 49

23. The equation of the regression line is   Solving and  

24. Scatter plot

25. Estimating the Value of y  

26. The slope and the y-intercept play important roles in estimating or predicting the value of the dependent variable. The amount of increase or decrease is indicated by the slope of the regression equation. The slope also indicates whether the correlation between the two variables is positive or negative.

27. The grades of 7 students in the first and second grading periods are shown below. Find the equation of the regression line. Estimate the grade in the second grading period of a student who received a grade of 88 in the first grading period. Example 6 x 80 78 76 82 84 85 75 y 84 79 75 86 84 77 78

28. solution x y xy 80 84 6720 6400 78 79 6162 6084 76 75 5700 5776 82 86 7052 6724 84 84 7056 7056 85 77 6545 7225 75 78 5850 5625 x y xy 80 84 6720 6400 78 79 6162 6084 76 75 5700 5776 82 86 7052 6724 84 84 7056 7056 85 77 6545 7225 75 78 5850 5625

29. The equation of the regression line is   Solving and  

30. Scatter plot The slope of 0.5 indicates that the correlation between the two variables is positive. If the regression line is drawn on the scatter plot, it will pass through 40.429 on the y-axis and it will be pointing upward to the right.

31. Estimating the Value of y