An economist is comparing the number of visitors (in 1000s) to the UK in a month, and the amount of money they spent ( millions). The

following results were obtained.

Number of visitors (1000s) 2450 2480 2540 2420 2350 2290 2400 2460 Amount of money spent ( millions) 1370 1350 1400 1330 1270 1210 1330 1350

(a) [1] Find the correlation coefficient between the amount of money spent and the number of visitors.

(b) [1] Give a reason to support fitting a linear regression model on the data set in terms of the result from (a).

(c) [1] Write down the fitted least squares regression equation to predict the amount of money spent from the number of visitors.

(d) [1] Interpret your value of slope in (c).

(e) [1] Construct a 90% confidence interval for the slope.

(f) [2] Does the the confidence interval in (e) provide sufficient evidence to indicate that there is a positive linear relationship between the amount of money spent and the number of visitors? Give the reason to get the full mark.

(g) [1] Estimate the amount of money spent when the number of visitors to the UK in a month is 2,500,000.

(h) [1] Give a 99% confidence interval for the average amount of money spent when the number of visitors to the UK in a month is 2,500,000.