2. Suppose I am interested in constructing a least squares regression line for 5 data points:...

Transcribed Image Text:

2. Suppose I am interested in constructing a least squares regression line for 5 data points: {(1,1), (3,2), (1,0.5), (0,0), (2,1.5)}. I do not have computer software available, so I am just going to take 3 guesses at my least squares regression line: 1: Y2X1 = 2: YX +1 3: Y = 1-3X + 1 a) Calculate the sum of the squared residuals for each of these 3 lines, and then... b) Identify which one of these three is the best choice for my least squares regression line. Note for Q3 and Q4: For Questions 3 and 4, it is relatively simple to find examples of variables with positive/negative correlation, but it is often difficult to tell whether the relationship will actually be linear versus some other type of correlation (quadratic, cubic, etc.), without actually getting data and running a hypothesis (which we don't want to do). For this reason, I will not be overly picky on this point. As long as there is some kind of correlation that could potentially be linear, I will accept the solution. 3. Give a real-life example of two variables X and Y that have a linear relationship between them, but it would be incorrect to conclude that X is affecting Y in any way or that Y is affecting X in any way. 4. When constructing a multilinear model, we want to avoid multicollinearity between the independent variables. Give a real-life example of 3 variables, Y, X, and X2, satisfying all the following conditions simultaneously: - There is a linear relationship between Y and X - There is a linear relationship between Y and X2 - There is no linear relationship between X and X2 5. Draw an example of a scatterplot with the given correlation coefficient: (Note: For b) and d), I will not be overly picky. A reasonable sketch is fine.) a) r = 0.98 b) r = 0.35 c) r = -0.98 d) r = -0.35 e) r = 0 2. Suppose I am interested in constructing a least squares regression line for 5 data points: {(1,1), (3,2), (1,0.5), (0,0), (2,1.5)}. I do not have computer software available, so I am just going to take 3 guesses at my least squares regression line: 1: Y2X1 = 2: YX +1 3: Y = 1-3X + 1 a) Calculate the sum of the squared residuals for each of these 3 lines, and then... b) Identify which one of these three is the best choice for my least squares regression line. Note for Q3 and Q4: For Questions 3 and 4, it is relatively simple to find examples of variables with positive/negative correlation, but it is often difficult to tell whether the relationship will actually be linear versus some other type of correlation (quadratic, cubic, etc.), without actually getting data and running a hypothesis (which we don't want to do). For this reason, I will not be overly picky on this point. As long as there is some kind of correlation that could potentially be linear, I will accept the solution. 3. Give a real-life example of two variables X and Y that have a linear relationship between them, but it would be incorrect to conclude that X is affecting Y in any way or that Y is affecting X in any way. 4. When constructing a multilinear model, we want to avoid multicollinearity between the independent variables. Give a real-life example of 3 variables, Y, X, and X2, satisfying all the following conditions simultaneously: - There is a linear relationship between Y and X - There is a linear relationship between Y and X2 - There is no linear relationship between X and X2 5. Draw an example of a scatterplot with the given correlation coefficient: (Note: For b) and d), I will not be overly picky. A reasonable sketch is fine.) a) r = 0.98 b) r = 0.35 c) r = -0.98 d) r = -0.35 e) r = 0