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Consider the data in the scatterplot below on the number of points scored (Y) and the number of goals scored (r) by Newcastle United in their last n = 10 seasons in the Premier League.

We also have the following summaries,

1. Based on the above scatter plot, describe briefly the relationship between points and goals. 2. Calculate , yJ, Sax, Syy and Say. 3. Hence calculate estimates of Bo, 31 and o2 in the simple linear regression model Yi Bo + Bixi + €i,=

4. Give an interpretation of the estimated parameter ₁ in the context of this example. -. Calculate the regression sum of squares. 5. Calculate the sample correlation coefficient, r. 7. Calculate the coefficient of determination, R2, and give an interpretation of this value. 5. How many points does the model predict that Newcastle United will achieve if they score 50 goals in the league by the end of the season? . As of 2nd February 2022, Newcastle United have scored 21 goals in the league. What does the model predict for the number of points they have scored up to this point? Comment onthe validity of this prediction.

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