statistics

(a) Suppose you fit a linear model to some sample data and find that the estimated slope = 1. 24. If there are 16 data points in your sample (n=16), the mean square error MSE=12 and Sxx=54 Compute the 95% confidence interval for the true population slope. (b) what is the purpose of calculating t-test for model utility? (c) A dataset contains information about the age (years) and height (cm) of 150 children. In order to relate the height of a child (Y) to the age of a child (X), a simple linear regression model is fitted to the data: E[Y ] = Bo + BIXi After fitting the model, the residuals are plotted, as shown below. 70 20 60 50 10 40 Residuals Frequency 30 O 20 -10 10 -20 0 -20 -10 0 10 20 4 6 8 10 12 14 16 Residuals Age Are the assumptions of the simple linear regression model are satisfied for this data