Answer the activity below with complete solutions

CONTENT We can predict the value of the dependent variable (Y) if we know the value of the independent variable (X). provided that these variables are significantly correlated. Such process is known as regression analysis. In regression analysis, the regression line (or trend line) must be determined. The line is the tool that is used in prediction; hence, it is sometimes called line predictor. The regression line is the same as the point-slope form equation of a line in Algebra. It is given by the equation Y = bX + a, where b is the slope and a is the y-intercept. EXAMPLES Example ! Example 2 In the regression line Y = 6X + 9, predict the value A significant relationship exists between the test of Y when the value of X is 7. scores in Mathematics (X) and the final grade in Solution: Mathematics (Y) of grade 11 learners. The regression Step 1. Copy the linear equation. line is given by the equation Y = 0.3X + 80.9. Predict Y = 6X +9 the final grade of a learner when her test score is 35. Step 2. Substitute the value of X in the equation Solution: Since X = 7. Step 1. Copy the linear equation. Y = 6(7) +9 Y = 0.3X + 80.9 Step 3. Solve for Y Step 2. Substitute the value of X in the equation Y = 42+9 Since X = 35, Y = 51 Y = 0.3(35) + 80.9 Therefore, we can predict that Y is 51 when X is 7. Step 3. Solve for Y Y = 10.5 + 80.9 Y = 91.4 Therefore, we can predict that the final grade of the learner is 91.4 (or 91) when she scores 35 in the Mathematics test. ACTIVITY Predict the value of Y given the regression line and the value of X in each item. 1. Y = 0.4X + 11;X = 2.5 2. Y = 21X + 123; X = 29 3. Y = 70X + 59; X = 38 4. Y = 0.43X + 1.1; X = 0.97 5. Y= XOX = 6. Assume that the height of fathers (X) and the height of their eldest sons (Y) were significantly correlated. The equation of the regression line is ) = 0.23X + 134. Given the height of your own father, predict the height of his eldest son. The height is expressed in centimeters