Jóhannes plans to examine the salary of a middle manager in a large company. He collects data on salaries and how long they have been employed as middle managers with the aim of creating a model that can predict salaries with work experience. Jóhannes has data from 20 randomly selected middle managers who range from being new to the job to having 12 years of work experience. Jóhannes started by drawing the data and sees that the relationship is linear. He also calculates some light sizes that can be seen below: Convert Average Standard deviation Salary 761041 238473 Job experience 5,65 3,71 He also calculated the correlation coefficient between wages and work experience and obtained a r = 0.82. a) Find an equal regression line for Jóhannes's model b) What is the explanatory power of the model and what does it tell us? c) How much does a middle manager's salary increase in five years according to the model?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Jóhannes plans to examine the salary of a middle manager in a large company. He collects data on salaries and how long they have been employed as middle managers with the aim of creating a model that can predict salaries with work experience. Jóhannes has data from 20 randomly selected middle managers who
| Convert | Average | Standard deviation |
| Salary | 761041 | 238473 |
| Job experience | 5,65 | 3,71 |
He also calculated the
a) Find an equal regression line for Jóhannes's model
b) What is the explanatory power of the model and what does it tell us?
c) How much does a middle manager's salary increase in five years according to the model?
d) Use the model to predict the salary of a middle manager with 20 years of work experience. Is the forecast reliable? Justify.
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