Question
Consider the following set of data points (Year of experience salary). Find the 2nd order polynomialand using polynomial regression determine the salary w
| Years of Experience (X) | Salary (Y) in Dollar |
| 1 | 50,000 |
| 2 | 55,000 |
| 3 | 65,000 |
| 4 | 80,000 |
| 5 | 110,000 |
| 6 | 150,000 |
| 7 | 200,000 |
hen year of experience is
Answer :
Word Count : 763
We are given data points: | X (Years) | Y (Salary) | | --------- | ---------- | | 1 | 50000 | | 2 | 55000 | | 3 | 65000 | | 4 | 80000 | | 5 | 110000 | | 6 | 150000 | | 7 | 200000 | We are to fit a second-order polynomial regression of the form: $$ Y = a_0 + a_1X + a_2X^2 $$ --- ### Step 1: Compute required summations Let’s compute the following: * $\sum X$ * $\sum X^2$ * $\sum X^3$ * $\sum X^4$ * $\sum Y$ * $\sum XY$ * $\sum X^2Y$ We'll construct a table: | X | Y | X² | X³ | X⁴ | XY | X²Y | | - | ------ | -- | --- | ---- | ------- | ------- | | 1 | 50000 | 1 | 1 | 1 | 50000 | 50000 __________ __________ __________ ________ ____ __________ ________.
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We are given data points: | X (Years) | Y (Salary) | | --------- | ---------- | | 1 | 50000 | | 2 | 55000 | | 3 | 65000 | | 4 | 80000 | | 5 | 110000 | | 6 | 150000 | | 7 | 200000 | We are to fit a second-order polynomial regression of the form: $$ Y = a_0 + a_1X + a_2X^2 $$ --- ### Step 1: Compute required summations Let’s compute the following: * $\sum X$ * $\sum X^2$ * $\sum X^3$ * $\sum X^4$ * $\sum Y$ * $\sum XY$ * $\sum X^2Y$ We'll construct a table: | X | Y | X² | X³ | X⁴ | XY | X²Y | | - | ------ | -- | --- | ---- | ------- | ------- | | 1 | 50000 | 1 | 1 | 1 | 50000 | 50000 __________ __________ __________ ________ ____ __________ ________.
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