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


Related Solutions

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 a. Regression eq: y=43.801+38.81X, where x=the number of years with the firm b. The standard error of estimate Sy,x=91.48. 1. The 95% confidence interval for x=10 for the average number of shares...
15.9 For a sample of 8 employees, a personnel director has collected the following data on...
15.9 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? For...
The personnel director for a small manufacturing company has collected the data found in the table...
The personnel director for a small manufacturing company has collected the data found in the table 1 describing the salary (Y) earned by each machinist in the factory along with the average performance rating (X1) over the past 3 years, the years of service (X2), and the number of different machines each employee is certified to operate (X3). The personnel director wants to build a regression model to estimate the average salary an employee should expect to receive based on...
The Company collected a sample of the salaries of its employees. There are 70 salary data...
The Company collected a sample of the salaries of its employees. There are 70 salary data points summarized in the frequency distribution below: Salary Number of Employees 5,001–10,000 8 10,001–15,000 12 15,001–20,000 20 20,001–25,000 17 25,001–30,000 13 Find the standard deviation. Find the variance.
a)The sales director has suggested using Big Data collected from market research and consumer activity on...
a)The sales director has suggested using Big Data collected from market research and consumer activity on social media. Critically evaluate the use of Big Data for sales forecasting b) Critically evaluate the usefulness of learning curve theory in the setting of selling prices. c) Critically evaluate the usefulness of management accounting techniques for decision making when future conditions are uncertain
Suppose the researcher has collected data from a sample of 150 individuals for this study. For...
Suppose the researcher has collected data from a sample of 150 individuals for this study. For each individual, the weekly take-home pay and weekly food expenditure were recorded. The data is stored in the file FOODEXP.XLS. Using this data set and EXCEL, answer the questions below. Take-home pay   Weekly food expenditure 262   82 369   182 374   144 381   161 378   210 395   126 401   196 410   212 408   130 415   151 418   145 415   171 425   156 116   114 120  ...
Consider the following data collected from four independent populations: Sample 1 Sample 2 Sample 3 Sample...
Consider the following data collected from four independent populations: Sample 1 Sample 2 Sample 3 Sample 4 3 14 21 8 8 9 15 3 6 13 16 13 5 14 a. Calculate the total sum of squares (SST). b. Partition the total sum of squares (SST) into its two components. c. Using a= 0.001, what conclusions can be made about the population means?
The Director of Sales purposefully collected data on two variables. These variables are simply identified as...
The Director of Sales purposefully collected data on two variables. These variables are simply identified as Y and X. Data on these two variables are summarized in the table presented below. Variable Y        Variable X 24 28 25 20 26 22 29 33 24 18 26 30 24 29 19 28 24 19 24 20 21 24 25 14 The Director approaches the Research Division for a validation of the speculative argument that ρ = 0, in the association...
The following data represent the salaries (in thousands of dollars) of a sample of 13 employees...
The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2. Calculate the interquartile range. What does this tell you about the data? Show your work. Describe the shape of distribution of salaries of employees of the firm based on the values of the quartiles. Give a possible reason for the shape of this data set, in terms...
The following data represent the time (in minutes) recorded for a sample of 20 employees in...
The following data represent the time (in minutes) recorded for a sample of 20 employees in order to get to work using public transportation. 12   37   24   5   9   42   46   39   54   34 22   50   58   30   27   118   61   47   18   15 (A) Does the sample contain any extreme values? Justify your answer with a suitable test. Comment on the results ... The sample Contains Extreme Values IQR = , Lower Limit = , Upper Limit = ,...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT