(a) What are the assumptions associated with the simple linear regression model?

(b) In a laboratory, the observation carried out on a sample of mice revealed their body weight (X) and their heart weight (Y) as follows:

Body weight (g) 30 37 38 32 36 38 42 36 41

Heart weight (mg) 118 136 140 122 131 136 145 135 142

(i) Draw a scatter diagram of the given data on graph paper and comment on the relationship between the body weight and the heart weight of the mice.

(ii) Find the equation of the estimated least squares regression line of y = a + bx and plot the line on the same graph as the scatter diagram. Interpret the values of a and b in your least squares regression line.

(c) Calculate the correlation coefficient and the coefficient of determination. State what does this indicate about the relation between body weight and the heart weight of mice.

(d) Estimate the likelihood of weight of the heart when the body weight of a mouse is:

(1) 35 grams

(2) 20 grams

Comment on the reliability of the estimates.