4)(5x4 = 20 points) The "HeightWeight" dataset contains height Y (in cm) and corresponding weight X (in kg) for a randomly selected group of 507 students. We will study the relationship between these two variables.

(a)Draw a scatterplot of the data (with the variables on the appropriate axes) and briefly describe the appearance of the plot.

(b)Fit a simple linear regression model to this data and report the estimated regression equation.

(c)Do a hypothesis test of H₀: ₀ = 0 vs. H₀: ₀ 0 at the = 0.05 significance level. Report the p-value and state your conclusion in the context of the problem.

(d)Do a hypothesis test of H₀: ₁ = 0 vs. H₀: ₁ 0 at the = 0.05 significance level. Report the p-value and state your conclusion in the context of the problem.

(e)Suppose we have a new student with weight x_h = 100 kgs. Using the model from part (b), what is the predicted height?