A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Salesperson Years ofExperience Annual Sales($1,000s) 1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10 119 8 10 123 9 11 117 10 13 136 (a) Develop a scatter diagram for these data with years of experience as the independent variable. A scatter diagram has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from 50 to 150 and is labeled: Annual Sales ($1,000s). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 1 to 13 on the horizontal axis and between 75 to 135 on the vertical axis. The points are fairly close together. A scatter diagram has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from 50 to 150 and is labeled: Annual Sales ($1,000s). 7 of the points are plotted from left to right in an upward, diagonal direction starting from the left side of the diagram and are between 1 to 10 on the horizontal axis and between 100 to 140 on the vertical axis. The other 3 points are plotted between 10 to 13 on the horizontal axis and between 80 to 100 on the vertical axis. In each group, the points are fairly close together. A scatter diagram has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from 50 to 150 and is labeled: Annual Sales ($1,000s). The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the diagram and are between 1 to 13 on the horizontal axis and between 80 to 140 on the vertical axis. The points are fairly close together. A scatter diagram has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from 50 to 150 and is labeled: Annual Sales ($1,000s). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 1 to 13 on the horizontal axis and between 80 to 140 on the vertical axis. The points are fairly close together. (b) Develop an estimated regression equation that can be used to predict annual sales (in $1,000s) given the years of experience. ŷ = (c) Use the estimated regression equation to predict annual sales (in $1,000s) for a salesperson with 9 years of experience. $ thousand
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.
Salesperson | Years of Experience |
Annual Sales ($1,000s) |
---|---|---|
1 | 1 | 80 |
2 | 3 | 97 |
3 | 4 | 92 |
4 | 4 | 102 |
5 | 6 | 103 |
6 | 8 | 111 |
7 | 10 | 119 |
8 | 10 | 123 |
9 | 11 | 117 |
10 | 13 | 136 |
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