Question
Consider the following set of data points (Year of experience salary). Find the 2nd order polynomial y=?0 + ?1?i + ?2 ?i 2 , and using polynomial regression determine the salary when year of experience is
| 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 |
Answer :
Word Count : 724
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We are to fit a 2nd order polynomial regression to the given data: $$ y = \beta_0 + \beta_1 x + \beta_2 x^2 $$ Where: * $x$ is the years of experience, * $y$ is the salary, * We need to find $\beta_0, \beta_1, \beta_2$, and * Use this to predict salary for any given year. --- ### Step 1: Create a table with required columns | $x$ | $y$ | $x^2$ | $x^3$ | $x^4$ | $xy$ | $x^2y$ | | ------- | ----------- | ------- | ------- | -------- | ------------- | -------------- | | 1 | 50,000 | 1 | 1 | 1 | 50,000 | 50,000 | | 2 | 55,000 | 4 | 8 | 16 | 110,000 | 220,000 | | 3 | 65,000 | 9 | 27 | 81 | 195,000 | 585,000 | | 4 | _________ ___ ______ __________ _____ _______ ___ _______.
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