Question

In: Statistics and Probability

For a sample of 8 employees, a personnel director has collected the following data on ownership...

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

  1. Determine the least-squares regression line and interpret its slope.

  2. 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.

Solutions

Expert Solution

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

__________________________________________

The Least square regression line is given by = b1x + b0, where b1 is the slope and b0 is the y coefficient

b1 the slope

_____________________

b0 the coefficient

___________________________

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

orchestra answered 2 years ago
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