Answer questions 5-10

Exercise 3. Are Foreign Companies "Buying Up the Canadian Economy"? (40 Marks) Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news breaks about a well-known Canadian company being purchased by a foreign competitor, with the implication that there will soon be no Canadian-owned companies left. In the following case study, we explore the relationship between the percentage of foreign ownership and year, using a simple linear regression analysis. One response has been for the Canadian government to try to regulate takeovers, making it more difficult for foreign companies to directly invest in Canada. At other times, the government has sought to encourage foreign investment by changing or rescinding regulations. For example, the Foreign Investment Review Agency was created in 1975 to monitor and regulate foreign takeovers in Canada. In 1985, after a change of government, the Foreign Investment Review Agency was replaced with a new agency, Investment Canada, whose mandate was intended to be less restrictive. Have these changes had any effect? The data in the table represent the percentage of commercial assets in non-financial corporations under foreign control y for the years 1975 to 2004. To simplify the analysis, we have coded the year using the coded variable r = year 1975. 1. 2 Marks] Using a scatterplot with Minitab, plot the data for the years 1975-1985. Does there appear to be a linear relationship between the percentage of foreign ownership and the year? 2. [3 Marks] Use Minitab to find the least-squares line for predicting the percentage of foreign ownership as a function of year for the years 1975-1985. 3. [2 marks] Is there a significant linear relationship between the percentage of foreign ownership and year at the level of significance of 5%? (Use the Minitab output from the previous question). 4.2 Marks] Use Minitab to predict the percentage of foreign ownership with 95% prediction intervals for the years 2002, 2003, and 2004. 5. [3 Marks] Now look at the actual data points for those years. Do the predictions obtained in step 4 provide accurate estimates of the actual values observed in these years? Explain. 6. 3 Marks) Using Minitab, construct the plot of residuals against the r values and then against the predicted values. What can you conclude about the validity of the constant variance assumption? 7. 3 Marks) Using Minitab, plot the histogram of the residualse, and the normal probability plot of residuals. What can you conclude about the normality assumption? 8. [4 Marks] Add the data for 1986-2004 to your database, and recalculate the regression line using again Minitab. What effect have the new data points had on the slope? What is the effect on SSE? 9. [3 Marks] Plot using Minitab the scatterplot of residuals against I, does it appear that a straight line provides an accurate model for the data? What model do the residuals indicate would produce a better fit? 10. 5 Marks] Plot using Minitab the data with a quadratic model fitted to them. Sketch what you consider to be the best-fitting linear or quadratic models? 11. [6 Marks) What is the increase in R when you fit a quadratic rather than a linear model? Is the coefficient of the quadratic term significant? Is the fitted quadratic model significantly better than the fitted linear model? (Use a = 0.05). 12. [4 Marks] Plot the residuals from the fitted quadratic model. Does there seem to be any apparent pattern in the residuals when plotted against x? Year x (year minus 1975) y (percent assets) 1975 0 30.2 1976 1 28.4 1977 2 28.3 1978 3 26.7 1979 4 26.8 1980 25.3 1981 G 23.4 1982 7 22.6 1983 8 22.3 1984 9 22.2 1985 10 21.4 1986 11 21.5 1987 12 22.5 1988 13 23.3 1989 14 23.6 1990 15 23.7 1991 16 23.6 1992 17 23.9 1993 23.8 1994 19 23.6 1995 20 25.1 1996 21 25.4 1997 22 25.9 1998 23 26.9 1999 24 25.3 2000 25 25.5 2001 26 28.8 2002 27 28.7 2003 28 28.7 2004 29 28.5 Exercise 3. Are Foreign Companies "Buying Up the Canadian Economy"? (40 Marks) Canada's for sale! We're losing our sovereignty! Dire statements such as these frequently appear in the media when news breaks about a well-known Canadian company being purchased by a foreign competitor, with the implication that there will soon be no Canadian-owned companies left. In the following case study, we explore the relationship between the percentage of foreign ownership and year, using a simple linear regression analysis. One response has been for the Canadian government to try to regulate takeovers, making it more difficult for foreign companies to directly invest in Canada. At other times, the government has sought to encourage foreign investment by changing or rescinding regulations. For example, the Foreign Investment Review Agency was created in 1975 to monitor and regulate foreign takeovers in Canada. In 1985, after a change of government, the Foreign Investment Review Agency was replaced with a new agency, Investment Canada, whose mandate was intended to be less restrictive. Have these changes had any effect? The data in the table represent the percentage of commercial assets in non-financial corporations under foreign control y for the years 1975 to 2004. To simplify the analysis, we have coded the year using the coded variable r = year 1975. 1. 2 Marks] Using a scatterplot with Minitab, plot the data for the years 1975-1985. Does there appear to be a linear relationship between the percentage of foreign ownership and the year? 2. [3 Marks] Use Minitab to find the least-squares line for predicting the percentage of foreign ownership as a function of year for the years 1975-1985. 3. [2 marks] Is there a significant linear relationship between the percentage of foreign ownership and year at the level of significance of 5%? (Use the Minitab output from the previous question). 4.2 Marks] Use Minitab to predict the percentage of foreign ownership with 95% prediction intervals for the years 2002, 2003, and 2004. 5. [3 Marks] Now look at the actual data points for those years. Do the predictions obtained in step 4 provide accurate estimates of the actual values observed in these years? Explain. 6. 3 Marks) Using Minitab, construct the plot of residuals against the r values and then against the predicted values. What can you conclude about the validity of the constant variance assumption? 7. 3 Marks) Using Minitab, plot the histogram of the residualse, and the normal probability plot of residuals. What can you conclude about the normality assumption? 8. [4 Marks] Add the data for 1986-2004 to your database, and recalculate the regression line using again Minitab. What effect have the new data points had on the slope? What is the effect on SSE? 9. [3 Marks] Plot using Minitab the scatterplot of residuals against I, does it appear that a straight line provides an accurate model for the data? What model do the residuals indicate would produce a better fit? 10. 5 Marks] Plot using Minitab the data with a quadratic model fitted to them. Sketch what you consider to be the best-fitting linear or quadratic models? 11. [6 Marks) What is the increase in R when you fit a quadratic rather than a linear model? Is the coefficient of the quadratic term significant? Is the fitted quadratic model significantly better than the fitted linear model? (Use a = 0.05). 12. [4 Marks] Plot the residuals from the fitted quadratic model. Does there seem to be any apparent pattern in the residuals when plotted against x? Year x (year minus 1975) y (percent assets) 1975 0 30.2 1976 1 28.4 1977 2 28.3 1978 3 26.7 1979 4 26.8 1980 25.3 1981 G 23.4 1982 7 22.6 1983 8 22.3 1984 9 22.2 1985 10 21.4 1986 11 21.5 1987 12 22.5 1988 13 23.3 1989 14 23.6 1990 15 23.7 1991 16 23.6 1992 17 23.9 1993 23.8 1994 19 23.6 1995 20 25.1 1996 21 25.4 1997 22 25.9 1998 23 26.9 1999 24 25.3 2000 25 25.5 2001 26 28.8 2002 27 28.7 2003 28 28.7 2004 29 28.5