The table below consists of 30 observations where each observation includes two values (Y and X). Please estimate the following linear formulation using the table below: Y = a + b X and please use the estimated model to predict the value of Y when X is 50. Y X 161 46 205 63 301 97 115 30 251 81 89 25 290 94 159 52 46 21 259 88 212 64 301 98 174 54 149 42 130 42 249 79 297 95 229 66 109 59 129 47 212 65 200 67 180 57 303 97 231 73 225 71 138 42 138 42 270 86 192 60 Question 2 options: 157.37 155.25 158.39 151.95 Save Question 3 (1 point) Question 3 Unsaved Please use the dataset from the table below to estimate the following linear regression model: Y = a + b X What is the residual for the very first observation in the dataset (Y=161, X=46)? Recall that the residual is the error, or the difference between the predicted value and the actual value. Y X 161 46 205 63 301 97 115 30 251 81 89 25 290 94 159 52 46 21 259 88 212 64 301 98 174 54 149 42 130 42 249 79 297 95 229 66 109 59 129 47 212 65 200 67 180 57 303 97 231 73 225 71 138 42 138 42 270 86 192 60 Question 3 options: 15.772 11.852 17.995 none of the above Save Question 4 (1 point) Question 4 Unsaved The table below contains 30 observations, each containing Y and X values. Please estimate the following linear regression model on this dataset: Y = a + b X In this estimation, what is the level of statistical significance for the intercept coefficient (a) to be different from zero? I.e., the level of confidence above which, the test where the null hypothesis is that the coefficient (intercept) is equal to zero, fails to reject the null. Y X 161 46 205 63 301 97 115 30 251 81 89 25 290 94 159 52 46 21 259 88 212 64 301 98 174 54 149 42 130 42 249 79 297 95 229 66 109 59 129 47 212 65 200 67 180 57 303 97 231 73 225 71 138 42 138 42 270 86 192 60 Question 4 options: 0.42361 0.57639 0.5653 5.630