The data below relates diamond carats to purchase prices.

Carat	0.31	0.32	0.36	0.38	0.4	0.43	0.45	0.48	0.5
Price	1641	1468	1685	1420	1797	1824	2043	2342	2122

Run a linear regression model, with the carat being the independent variable ( X ) and the purchase price being the dependent variable ( Y ).

(a) Find the estimate of the intercept for the linear regression model.

(b) Find the estimate of the slope for the linear regression model.

(c) What is the predicted price of a 0.37 carat diamond?

(d) What fraction of the dependent variable's variation can be explained by this linear regression model?