Quarter: 5 Week: g MELQS): 1. Calculates the slope and y-interoept of the regression line (MHHZSP-Wi-JJ; 2. Interprets the calculated slope and y-intercept of the regression line {M1123PfVI4); 3. Predicts the value of the dependent variable given the value ol the independent variable (MHZSPWJt); and 4. Solves problems involving regression analysis {M112SP-lW-2J > Title of Textbook\" to Study: W > Chapter: l Pages: M Topic: imple Linear Regression it Objectives: 1. To interpret the calculated slope and y-intercept of the regression line. 2. To predict the value of the dependent variable given the value of independent variable. 3. To solve problems involving regression analysis. If two variables are signicantly correlated, then we can predict the value of one variable (1-, independent variable) in terms ofthe other variable ()1, dependent variable). Thus, we can perform regression analysis. Regression analysis is a set o1 statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. With regression analysis you can see trends that can be harnessed for data prediction. Below is the Linear Regression Equstlon. In the equation belowa is y |nteroept and b is the slope; these are the regression coefficients. The slope of a regression line (b) represents the rate of change in y as 1 changes. Because )1 is dependent on x. the slope describes the predicted values of y given :1 where: my\"; J\" = bx + (I. y' = dependent variablefpredicted value Equation x = value of the independent variable n = number of variables 5101'\" (b) 01' y = dependent variable values = any- (220610 Regresslon b a = y-intercept of the regression line _ z n 2 x2 (2 x) b = slope of the regression line Jutemgpf g j = mean of the dependent variables Jr {J a : T _ hi i: mean of the independent variables GSC-CJDLm-ESSLM, VJ. 52.00, E'ectfve 14.011121, 2:221 Having values for the slope and yhintercept ofthe regression line, we can then predict the value of y for a given value of 1 using the regression line function. Example 1. The sales of a company (in million Pesos) for each thousands of car sold are shown in the table below. Solve for the slope of the regression line and the yintercept, then predict the sales if the company sold 25 thousand units. Cars x Sales y 2 0mm\" (in thousands} (in millions} \"Y x 1 63 r 441 3939 2 29 3.9 113.1 341 3 20.8 2.1 43.68 432.64 4 19.1 1.4 23.74 364.31 5 13.4 1.5 20.1 179.56 5\"" 12m) \"0" 145.30 15.90 544.52 57117.01 Mean 29.08 3.18 Having the values for the slope and y-interoeptwe can then use the Linear Regression Equation to the predict the sales of 25 thousand units. Given: Ex: 145.30 Ey=15.90 f = 29.05 21)! = 644.62 22:2 = $87.01 Safuon: 37:3.18 n=5 17:16 f 5.00 KB/S 26 111 39 Having the values for the slope and y-intercept we can then use the Linear Regression Equation to the predict the sales of 25 thousand units. Given: Ex = 145.30 Ey = 15.90 Exy = 644.62 Ex2 = 5787.01 * = 29.06 y = 3.18 n =5 Solution: b =. nExy - ( Ex) (Ey) a = y - bx nEx2 - (Ex)2 a = (3.18) - (0.116686) (29.06) b =. (5) (644.62) - (145.30) (15.90) a= -0.210895 (5) (5787.01) - (145.30)2 912.83 b 7822.96 b = 0.116686 or 0.12 y' = bx + a y' = (0.116686) (25)+ (-0.210895) y' = 2.70625 Interpretation: Using the given data, we were able to predict the sales for 25 thousand units which amounts to 2.70625 million. GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 Let Us Try Activity 1: Calculate and Predict A. Calculate the slope and y-intercept given the following data. 1. n = 6,Ex = 153.8 Zy = 18.7, Exy = 682.77,Ex^2 = 5859.26 2. n = 7, x = 57 Zy = 511, Exy = 3745, _ x2 = 579 B. Given the solved data above, generate the Linear Regression Equation and predict the y' for the given values of x. 3. y' = (b)x + (a); where, x = 50 4. y' = (b)x + (a); where, x = 10 > > Let Us Do Activity 2: Fill in the blanks Below are the scores of five students in Math with its corresponding its grade. If a student gets 20 correct items, what will be their corresponding grade? Student Correct items (x Grade (y) xy x2 A 11 80 B 13 85 C 19 90 16 87 F 21 95 Summation ()) Mear Given: Solution O17:16 f 0.70 KB/S 39 Given: Solution 1. Ex = 2. Ey = b = " n Exy - ( Ex)In y' = bx + a nEx2 - (Ex)2 a = y - bx 3. Exy = 7. b = 8. 0= 9. y = 4. Ex' = 5. x = 6. y= Interpretation: Therefore, the grade of the student who obtained 20 correct items is _. (10) GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 Let Us Apply Activity 3: In real life 1. It is undeniable that the Covid-19 pandemic shook us to our core. The cost of mostly all things increased. Using the data below predict the possible insurance cost for the age 29. Ages (X) Insurance cost (Y) 19 1000 22 120 30 2000 27 1575 23 1250 References Elementary Statistic by Allan Bluman SSLM Development Team Writer: Glerry Paul G. Borja Evaluator: Marjohn C. Mantawil Illustrator: Glerry Paul G. Borja Creative Arts Designer: Reggie D. Galindez Education Program Supervisor - Mathematics: Zaida N. Abiera > > Education Program Supervisor - Learning Resources: Sally A. Palomo Curriculum Implementation Division Chief: Juliet F. Lastimosa Asst. Schools Division Superintendent: Carlos G. Susarno, Ph. D. Schools Division Superintendent: Romelito G. Flores, CESO V GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 E O