Question:
Consider the linear regression model yi = β0 + β1xi + ∈i , i = 1, 2, … , 6, where β0 and β1 are unknown parameters and ∈i ’s are independent and identically distributed random variables having N(0, 1) distribution. The data on (xi, yi) are given in the following table.xi 1.0 2.0 2.5 3.0 3.5 4.5 yi 2.0 3.0 3.5 4.2 5.0 5.4
If \(\hat{\beta}_0\) and \(\hat{\beta}_1\) are the least squares estimates of β0 and β1, respectively, based on the above data, then \(\hat{β}0 + \hat{β}1\) equals __________ (round off to 2 decimal places)
Consider the linear regression model yi = β0 + β1xi + ∈i , i = 1, 2, … , 6, where β0 and β1 are unknown parameters and ∈i ’s are independent and identically distributed random variables having N(0, 1) distribution. The data on (xi, yi) are given in the following table.
If \(\hat{\beta}_0\) and \(\hat{\beta}_1\) are the least squares estimates of β0 and β1, respectively, based on the above data, then \(\hat{β}0 + \hat{β}1\) equals __________ (round off to 2 decimal places)
| xi | 1.0 | 2.0 | 2.5 | 3.0 | 3.5 | 4.5 |
| yi | 2.0 | 3.0 | 3.5 | 4.2 | 5.0 | 5.4 |
Updated On: Oct 1, 2024
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Correct Answer: 2
Solution and Explanation
The correct answer is 2.00 to 2.10.(approx)
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