25155 I O 4 Quarter: 1 Week: g MELC(S): 1. Calculates the slope and y-intercept of the regression line {M1128P-iW3J; 2. Interprets the calculated slope and v-intercept of the regression line {M1128P-fVi4); 3. Predicts the value of the dependent variable given the value of the independent variable {M1 tZSP-il-n; and 4. Solves problems involving regression analysis (M1 tzSP-WJz) > Title of Textbooki'LM to Study: Statistics and Probabilitg > Chapter: 10 Pages: {53% Topic: imple Linear Raression > Oblectlves: 1. To interpret the calculated slope and yintercept 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 significantly correlated, then we can predict the value of one variable (1. independent variable) in terms of the other variable ()1, dependent variable). Thus, we can perform regression analysis. Regression analysis is a set of statistical methods used for the estimation of relationsh'ps between adependent 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 Equation. In the equation below a is y -intercept 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 31 is dependent on x, the slope describes the predicted values of y given 7: where: y' = dependent variableipredicted value x = value of the independent variable :1 = number of variables y = dependent variable values 0 = y-intercept of the regression line b: slope ol the regression line 3'; = mean of the dependent variables at: mean of the independent variables Regression Equation y'=bx+a slope (b) of _ may 0 -w Line TI 2 x2 _ (E 37): y-fnmf (a) ofRegnession at: 7 bf Line GSCCiDtRMSESSLM, IIJ. 200, EffecthmAani 21', 2152'! Having values for the slope and yhintercept of the regression line, we can then predict the value of y for a given value of .11 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. Sohie for the steps of the regression line and the y-intercept, then predict the sales if the companyr sold 25 thousand units. Cars x Sales v 2 \"mp3"? (in thousands) {in millions) '9' I 1 63 7 M1 3939 2 29 3.9 113.1 341 3 20.3 2.1 43.63 432.64 4 19.1 1.4 26.74 364-31 5 13.4 1.5 20.1 170.50 SW???\" 145.30 15.00 044.02 5737.01 Mean 29.06 3.18 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. GIVE"! 2x =145.3u 5331:1590 Exy=64d.62 2x2 = 5737.01 Solution: i=29.06 7:3.10 n=5 23:53 0.25 KB/S 26 11 43 Solution: b = - nExy - () x) (Zy) a = y - bx nEx - (Ex)2 a = (3.18) - (0.116686) (29.06) (5)(644.62) - (145.30) (15.90) b = a = -0.210895 (5) (5787.01) - (145.30)2 912.83 b = 7822.96 b = 0.116686 or 0.12 y' = bx + a y' = (0.1 16686)(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,Ex = 57 Zy = 511, Exy = 3745,Ex? = 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 Grade (y) xy x2 X A 11 80 13 85 19 90 D 16 B7 m 21 95 Summation (X) Mean Given: Solution 1. E x = 2. Ey = b = _ nExy - ( x)(Im y' = bx + a nEx2 - (Ex)2 a = y- bx 3. Exy = 8. a = 9. y = 4. E x2 = 7. b = 5. x = 6. y = E O23:53 N 0.59 KB/S 6 11 43 1. Ex = b = _ nExy - ( x)(Im y' = bx + a 2. Ey = nEx2 - (Ex)2 a = y - bx 3. Exy = 9. y' = _ 4. E x2 = 7. b =_ 8. a =_ 5. X = 6. V = 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 1200 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 4 of 4 GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 E O