1.3 Table 1 below, presents the total salaries (in million pounds) and the number of points...

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1.3 Table 1 below, presents the total salaries (in million pounds) and the number of points earned for 20 English Premier League teams in 1995/6. Table 1 English Premier League Teams data Team's name Arsenal Aston Villa Blackbur Bolton Chelsea Coventry Everton Leeds Liverpool Manchester City Manchester United Middlesbrough Newcastle Nottingham Forest Queen's Park Sheffield Southampton Tottenham West Ham Unit Wimbledon Salary (x, 000 000) 10.1 7.7 10.8 3.3 9.2 5.8 10.1 10.1 13.2 64 13.3 6.5 19.7 8.5 5 4.1 9.8 6.2 4.7 Points earned (y) 63 63 628 357 61 29 50 38 61 43 71 38 82 43 78 58 33 40 38 61 51 41 Take note of the following results that were obtained from the dataset above 20 170.9 X'X = [170.9 1749.15 1042 and X'Y Y = [193], then answer the questions that follow: 19870.3 1.3.1 Compute (X'X)-¹ and 3. (4) Give the fitted equation for the simple linear model y = Bo + B₁x + e fitted on the dataset and interpret the coefficients. (4) 3 STA3701/012/0 Is the salary paid to the team a significant predictor of the number of points earned by a team? Test this at the 5% level of significance. (Hint: Test the hypotheses Ho: P₁0 vs H₁:₁0.) For this test, give the test statistic, rejection region and conclusion. (6) 1.3.4 Construct a 95% confidence interval for ₁. Does this result support your answer in question 1.3.3? Explain. (6) 1.3 Table 1 below, presents the total salaries (in million pounds) and the number of points earned for 20 English Premier League teams in 1995/6. Table 1 English Premier League Teams data Team's name Arsenal Aston Villa Blackbur Bolton Chelsea Coventry Everton Leeds Liverpool Manchester City Manchester United Middlesbrough Newcastle Nottingham Forest Queen's Park Sheffield Southampton Tottenham West Ham Unit Wimbledon Salary (x, 000 000) 10.1 7.7 10.8 3.3 9.2 5.8 10.1 10.1 13.2 64 13.3 6.5 19.7 8.5 5 4.1 9.8 6.2 4.7 Points earned (y) 63 63 628 357 61 29 50 38 61 43 71 38 82 43 78 58 33 40 38 61 51 41 Take note of the following results that were obtained from the dataset above 20 170.9 X'X = [170.9 1749.15 1042 and X'Y Y = [193], then answer the questions that follow: 19870.3 1.3.1 Compute (X'X)-¹ and 3. (4) Give the fitted equation for the simple linear model y = Bo + B₁x + e fitted on the dataset and interpret the coefficients. (4) 3 STA3701/012/0 Is the salary paid to the team a significant predictor of the number of points earned by a team? Test this at the 5% level of significance. (Hint: Test the hypotheses Ho: P₁0 vs H₁:₁0.) For this test, give the test statistic, rejection region and conclusion. (6) 1.3.4 Construct a 95% confidence interval for ₁. Does this result support your answer in question 1.3.3? Explain. (6)