Suppose we wish to predict the profits, in hundreds of thousands of dollars, for companies that had sales, in hundreds of thousands of dollars, of 500 units. We use statistical software to do the prediction and obtain the displayed output. St. dev. mean Sales Predict predict 95% C.I. 95% P.I. 500 -130.4 59.3 (-248.5,-12.3) (-1066.4, 805.6) A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales, in hundreds of thousands of dollars, and profits, in hundreds of thousands of dollars, was investigated by regression. The simple linear regression model displayed was used: profits = a + B (sales), where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation o. This model was fit to the data using the method of least squares. The results displayed were obtained from statistical software. 2 = 0.662 s = 466.2 Parameter Std. err. of Parameter estimate parameter est. -176.644 61.16 0.092498 0.0075 A 95% contidence interval for the average profit of companies with 500 units of sales is: C-1066 Ato 805 6
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.
![Suppose we wish to predict the profits, in hundreds of thousands of dollars, for companies that had sales, in hundreds of
thousands of dollars, of 500 units. We use statistical software to do the prediction and obtain the displayed output.
St. dev. mean
Sales Predict
predict
95% C.I.
95% P.I.
500
-130.4
59.3
(-248.5,-12.3)
(-1066.4, 805.6)
A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales, in hundreds of
thousands of dollars, and profits, in hundreds of thousands of dollars, was investigated by regression. The simple linear
regression model displayed was used: profits a + ß (sales), where the deviations were assumed to be independent and
Normally distributed, with mean 0 and standard deviation o. This model was fit to the data using the method of least
squares. The results displayed were obtained from statistical software.
2= 0.662
s = 466.2
Parameter
Std. err. of
estimate
parameter est.
Parameter
-176.644
61.16
0.092498
0.0075
A 95% confidence interval for the average profit of companies with 500 units of sales is:
-1066 41n 805 6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fb7a5f7-d1fe-47c3-ab51-c010c8f81dff%2Fb74c36ce-429b-4a5d-a516-860a7d42b53a%2Fkrafowo_processed.jpeg&w=3840&q=75)
![A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales, in hundreds of
thousands of dollars, and profits, in hundreds of thousands of dollars, was investigated by regression. The simple linear
regression model displayed was used: profits
= a + B (sales), where the deviations were assumed to be independent and
Normally distributed, with mean 0 and standard deviation o. This model was fit to the data using the method of least
squares. The results displayed were obtained from statistical software.
2 = 0.662
S= 466.2
Parameter
Std. err. of
Parameter
estimate
parameter est.
-176.644
61.16
0.092498
0.0075
A 95% confidence interval for the average profit of companies with 500 units of sales is:
-1066.4to 805.6.
O -189.7 to -71.1.
400.7 to 559.3.
-248.5 to -12.3.
delete](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fb7a5f7-d1fe-47c3-ab51-c010c8f81dff%2Fb74c36ce-429b-4a5d-a516-860a7d42b53a%2Fm7i51ue_processed.jpeg&w=3840&q=75)
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