Prepare a test, which will cover the topic below:
Business statistics (descriptive statistics and inferential statistics on least squares methods (regression line))
Component of the test:
Application (40 marks)
1. Calculate the mean, median, mode, range, variance, and standard deviation for the following data set: 15, 20, 25, 30, 35, 40, 45, 50.
2. Construct a frequency distribution table and histogram for the following data set: 10, 15, 20, 25, 30, 35, 40, 45, 50.
3. Calculate the correlation coefficient between two variables X and Y using the following data:
X: 10, 15, 20, 25, 30
Y: 20, 25, 30, 35, 40
4. Perform a simple linear regression analysis using the least squares method on the following data:
X: 1, 2, 3, 4, 5
Y: 3, 5, 7, 9, 11
5. Interpret the coefficient of determination (R^2) and the standard error of estimate in the regression analysis in question 4.
6. Given the regression equation Y = 2X + 1, predict the value of Y when X = 10.
7. Conduct a hypothesis test to determine if there is a significant relationship between X and Y in the regression analysis from question 4. Use a significance level of 0.05.
8. Discuss the assumptions of the linear regression model and explain why they are important in interpreting the results of a regression analysis.
9. Calculate the confidence interval for the slope of the regression line in question 4.
10. Provide a real-life example where regression analysis can be applied in a business setting and explain how it can help in making informed decisions.
Note: Each question is worth 4 marks, totaling 40 marks for the application component of the test. Make sure to show all calculations and provide clear explanations for each question.