Question 1 (8 marks) Insurance companies use actuarial tables to estimate the remaining lifespans of their customers. The table below presents estimated additional years of life for a certain population. Age 10 20 30 40 50 60 70 80 90 100 Years Left 60.3 50.7 41.8 32.9 24.8 17.9 12.1 7.9 5.0 3.0 a) Create a scatter plot of this data and add a linear regression line to the scatterplot. (2 marks) b) Discuss if a linear regression model is an appropriate model to use for the dataset. (2 marks) c) Re-express the variable 'Years left' using a square root. Create a scatterplot of 'Age' and the square root of 'Years left'. Add a regression line to the scatterplot. (2 marks) d) Find the equation of the regression line from c) and predict the remaining lifespan of a 24-year-old member of the population. (2 marks) The most common theory explaining global warming relates an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas, to increases in temperature. Data about two variables were collected: the mean annual CO2 concentration in the atmosphere, measured in parts per million (ppm), and the mean annual air temperature across the globe, measured in degrees Celsius. A regression predicting temperature from CO2 concentration using the above data produced the following output table. Both coefficients were found to be statistically significant. Dependent variable is: Temperature R-squared 64.1% Variable Intercept CO Coefficient 15.21 0.020 a) What percentage of variability in the temperature does this model explain? (2 marks) b) Give the regression equation. Name variables clearly. (2 marks) c) What is the meaning of the slope in this equation? (2 marks) d) If CO2 levels reach 410 ppm, what mean temperature would the regression model predict? (2 marks) e) How would you check whether a regression model is appropriate for this analysis? (3 marks)