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The last line of the code above corresponds to creating a linear model in which y is a function of 1:1 and x2

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The last line of the code above corresponds to creating a linear model in which y is a function of 1:1 and x2 . Write out the form of the linear model. What are the values of the regression coe?icients ?u, 31 and ,82? What is the value of 02'? b. (2 pts) Use the function cor? to calculate the correlation coef?cient between x1 and x2. Create a scatter plot using ggplo't2 displaying the relationship between the variables x1 and x2 . What can you say about the dierction and strength of their relationship? a. c. (4 pts) Fit a least squares regression to predict 3; using x1 and x2 . Describe the obtained results. What are the values of fig, 31 and 32? How do these relate to the the values of ?g. ,31 and ?g? What is the value of 3 and how does it relate to the the value pro-2? Can you reject the null hypothesis Hg. : £1 = 0? How about the null hypothesis Hg : [3'2 2 I]? d. (3 pts) Now ?t a least squares regression to predict y using only x1 . Comment on your results. What are the values of ?n and 31? HOW do these relate to the tme values of ?n and 31? What is the value of .5 and how does it relate to the true value of 0-2 ? Can you reject the null hypothesis Ho : :31 = I]? e. (3 pts) Now ?t a least squares regression to predict 3- using only x2 . Comment on your results. What are the values of ?n and 32? How do these relate to the tme values of ?n and 32? What is the value of 3 and does it relate to the tme value ofo2 ? Can you reject the null hypothesis H" : '82 = 0'?