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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 1250Let Us Discover If two variables are significantly correlated, then we can predict the value of one variable (x, independent variable) in terms of the other variable (y, dependent variable). Thus, we can perform regression analysis. Regression analysis is a set of 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 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 x changes. Because y is dependent on x, the slope describes the predicted values of y given x where: Regression Equation y' = bx + a y' = dependent variable/predicted value x = value of the independent variable n = number of variables Slope (b) of Regression nExy - (Ex)(Zy) y = dependent variable values Line n Ex - (Ex)2 a = y-intercept of the regression line b = slope of the regression line y-Intercept (a) y = mean of the dependent variables of Regression a = y - bx *= mean of the independent variables Line GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 Having values for the slope and y-intercept of the regression line, we can then predict the value of y for a given value of x 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 y-intercept, then predict the sales if the company sold 25 thousand units. Company Cars x Sales y (in thousands) (in millions) xy x2 63 7 441 3969 2 29 3.9 113. 841 3 20.8 2.1 13.68 432.64 4 19.1 1.4 26.74 364.81 5 13.4 1.5 20.1 179.56 Summation 145.30 15.90 644.62 (2 5787.01 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. Given: Ex = 145.30 Ey = 15.90 Exy = 644.62 Ex2 = 5787.01 * = 29.06 y = 3.18 n =5 Solution: b = ! nExy - (Ex)(Zy) a = y - bx nEx2 - (Xx)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' = (0.116686) (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