A doctor wants to test the relationship between the daily consumption of cigarettes (variable X) and...

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A doctor wants to test the relationship between the daily consumption of cigarettes (variable X) and the number of sleep hours (variable Y). The following data shows the sums of the study for a population of 50 individuals: k i=1 k k == xini = 600 ΣΣx y, ny = 3930 * ' nij i=1 j=1 h Σ y; ⋅ n; = 350 Σy; j=1 k Σ x ² • ni i=1 = 7650 h ynj = 2650 a) Find the population mean and the population standard deviation for each variable. Justify your answer and interpret all the results. (0.75 points) b) Calculate the population covariance between X and Y and the linear correlation coefficient. Justify your answer and interpret all the results. (0.75 points) c) If we define two new variables, A and B, which both are linear transformations -2y;-7. What would be the 1 4x₁ - ½ and bj 2 = 3 of the initial variables: a; = = population covariance between A and B? (0.5 points) A doctor wants to test the relationship between the daily consumption of cigarettes (variable X) and the number of sleep hours (variable Y). The following data shows the sums of the study for a population of 50 individuals: k i=1 k k == xini = 600 ΣΣx y, ny = 3930 * ' nij i=1 j=1 h Σ y; ⋅ n; = 350 Σy; j=1 k Σ x ² • ni i=1 = 7650 h ynj = 2650 a) Find the population mean and the population standard deviation for each variable. Justify your answer and interpret all the results. (0.75 points) b) Calculate the population covariance between X and Y and the linear correlation coefficient. Justify your answer and interpret all the results. (0.75 points) c) If we define two new variables, A and B, which both are linear transformations -2y;-7. What would be the 1 4x₁ - ½ and bj 2 = 3 of the initial variables: a; = = population covariance between A and B? (0.5 points)