1. 2. State instances in real life where we have correlation between two variables X and Y. State the formula for correlation coefficient between two variables X and Y and show that r remains invariant under affine transformation of X and Y. ziri ni bazu dT gida (Hint: Let X*=a+bX and Y* =c+Yd. Show that the correlation between X* and Y* is the same between X and Y) 3. Ten students sat for physics and calculus and the 4. scores are as given below. 85 77 Physics 58 70 65 85 77 55 55 40 40 62 82 86 60 82 74 50 38 38 60 60 83 84 Calculus 55 64 64 60 a) Calculate the correlation coefficient r between the two courses b) Add 2 to all numbers in the above table and re c) calculater If scores in physics and calculus are respectively given by Y and X how much of variation in Y is accounted for by X? Draw a scatter diagram for data in problem 3. Is a linear relationship between X and Y suitable? abem 1. Consider the simple regression model 2.0A Y = B + BX + u 80 2.18 S.88 0.28 8.AE 2.46 Why do we incorporate the error term u in the above model? 8.T st Mention four instances in real life where regression 2. is applied. DATA