West Edmonton Mall, located in Edmonton, Canada, is the largest shopping mall in North America. The mall attracts thousands of shoppers daily. The actual daily visitor number depends on the day and season. Does the cold weather have any effect on the number of visitors, and eventually the retail business of the mall? In order to investigate this, suppose a sample of 6 weekdays was randomly selected from January 2019 to February 2019. The number of shoppers/visitors (in thousands) and the mean temperature (°C) were recorded for each of the selected days as shown in the following table. Day Mean Temperature Number of Visitors (°C) in thousands) ly) (x) February 8 January 25 February 29 January 4 January 17 January 10 -8.7 -1.3 -13.4 4.9 -29.4 -4.9 90 76 46 128 16 106
To save computational time, you may use the following sums and sums of squares and cross- products for subsequent calculations: Ex = -52.8 Ey = 462 SSxx = 704.68 SSyy = 8,294 SSxy = 2,204.8 a. Find the values of a and b in the least square line y=a + bx for predicting the Number of Visitors as a function of Mean Temperature. (Note: Enter the values of a and b rounded to at least 2 decimal places of accuracy.) Least square regression line: y = a + bx a = Number b = Number 6. Use the equation of the regression line in part (a) to predict "Number of Visitors" if the "Mean Temperature" is -20 °C. (Note: Enter the numerical value rounded to at least 2 decimal places of accuracy, do not convert to thousands.) Number
b. Find a 99 % confidence interval for the slope B. (Note: Write your answer in interval form (m, n), where m and n are round to three decimals.) 99 % confidence interval for the slope: (Lower Value = Number Upper Value = Number c. Test at the 1% significance level whether the slope B is positive. Complete the table below, round t-values to three decimals. Hypotheses Ho: B=0, H1: B > 0 Critical Number Value oft Test Statistic Number Value Yes Reject Ho? No Conclude that the slope of the regression line is positive.
je no O NO Conclude that the slope of the regression line is positive. Conclusion Cannot conclude that the slope of the regression line is positive. d. Compute the linear correlation coefficient between "Number of Visitors (y)" and "Mean Temperature (x)". (Note: Enter the numerical value rounded to at least 2 decimal places of accuracy.) Number e. Approximately what percent of the variation in 'Number of Visitors' is explained by its linear relationship with 'Mean Temperature'? (Note: Enter the nearest whole number percentage value without the percent sign.) Number