In: Statistics and Probability
For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock versus years with the firm.
x = 5 Years
6 12 14 6 9 13 15 9
y = 5 Shares
300 408 560 252 288 650 630 522
Determine the least-squares regression line and interpret its slope.
For an employee who has been with the firm 10 years, what is the predicted number of shares of stock owned?
Please show me (a) your summary statistics; (b) how you use the summary statistics to compute the slope and the intercept of the regression line.
The Summary statistics are given below
Count | x | y | xy | x2 |
1 | 6 | 300 | 1800 | 36 |
2 | 12 | 408 | 4896 | 144 |
3 | 14 | 560 | 7840 | 196 |
4 | 6 | 252 | 1512 | 36 |
5 | 9 | 288 | 2592 | 81 |
6 | 13 | 650 | 8450 | 169 |
7 | 15 | 630 | 9450 | 225 |
8 | 9 | 522 | 4698 | 81 |
Total | 84 | 3610 | 41238 | 968 |
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The Least square regression line is given by = b1x + b0, where b1 is the slope and b0 is the y coefficient
b1 the slope
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b0 the coefficient
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Therefore the least square regression line is = 38.756x + 44.314.
The slope is interpreted as the rate of change in y, for every unit increase of x
If x = 10, then the predicted number of shares = (38.756 * 10) + 44.314 = 431.874 432 shares