3. (3 Points) Least Squares Regression. (Note: This problem is similar but not iden- tical to Question 3 on Homework #11.) Suppose that in a certain chemical process the reaction time Y (hours) is measured in response to the temperature x (degrees Fahrenheit, F). The data are assumed to fit a linear model and you will use R to: (1) Generate synthetic data (i.e., you know the answer!) (2) Fit a linear model to the data. (3) Analyze the linear model. In the chamber in which the reaction takes place according to the simple linear re- gression model: Y = 5.00 0.01c+U where U is the error in the reaction time and is known to be normally distributed with mean 0 and 62 = = (0.075) Since in simple linear regression we assume that the independent variable in this case temperature) is known exactly, we can also write: Yz = 5.00 0.01x + U. (a) (1 Point) Determine confidence intervals in the estimate of your values for a and B. (b) (1 Point) Increase the number of points you sample, how does this impact the ability to estimate the correct parameters? Do the confidence intervals change? Give another set of estimates for a and B for your new choice. (c) (1 Point) Decrease the number of points you sample (less than 30) and increase the variance in the noise U. How does this impact the ability to estimate the correct parameters? Give another set of estimates for a and B for your new choice. 3. (3 Points) Least Squares Regression. (Note: This problem is similar but not iden- tical to Question 3 on Homework #11.) Suppose that in a certain chemical process the reaction time Y (hours) is measured in response to the temperature x (degrees Fahrenheit, F). The data are assumed to fit a linear model and you will use R to: (1) Generate synthetic data (i.e., you know the answer!) (2) Fit a linear model to the data. (3) Analyze the linear model. In the chamber in which the reaction takes place according to the simple linear re- gression model: Y = 5.00 0.01c+U where U is the error in the reaction time and is known to be normally distributed with mean 0 and 62 = = (0.075) Since in simple linear regression we assume that the independent variable in this case temperature) is known exactly, we can also write: Yz = 5.00 0.01x + U. (a) (1 Point) Determine confidence intervals in the estimate of your values for a and B. (b) (1 Point) Increase the number of points you sample, how does this impact the ability to estimate the correct parameters? Do the confidence intervals change? Give another set of estimates for a and B for your new choice. (c) (1 Point) Decrease the number of points you sample (less than 30) and increase the variance in the noise U. How does this impact the ability to estimate the correct parameters? Give another set of estimates for a and B for your new choice