a. (1) time is the dependent variable or (2) Marks is the dependent variable b. Calculate c. Determine the least squares estimator for i.e, Answer d. (1) Based on the value for , the independent variable does not have an influence on the dependent variable. (2) Based on the value for , an increase of the independent variable will result in a decrease of the dependent variable. (3) Based on the value for , an increase of the independent variable will result in an increase of the dependent variable. e. Determine the least squares estimator for i.e,
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.
Mr. Smith continues on his project of gaining insights on the 2020 BIOLOGY class and now that the first test has been written he can get initial findings. Something of interest that he would like to explore is the relationship between marks obtained and the time taken to complete the Test 1. In particular, he wants to answer: what influence does marks obtained have on the amount of time taken to finish the Test 1 . The table below shows a randomly selected sample of results for 12 students:
| Marks (%) | Time (mins) |
|---|---|
| 57 | 33 |
| 67 | 29 |
| 83 | 26 |
| 100 | 21 |
| 23 | 43 |
| 40 | 43 |
| 43 | 21 |
| 47 | 38 |
| 33 | 44 |
| 60 | 36 |
| 57 | 30 |
| 53 | 40 |
Use this data to answer the following questions:
a. (1) time is the dependent variable or (2) Marks is the dependent variable
b. Calculate
c.
Determine the least squares estimator for i.e, Answer
d.
(1) Based on the value for , the independent variable does not have an influence on the dependent variable.
(2) Based on the value for , an increase of the independent variable will result in a decrease of the dependent variable.
(3) Based on the value for , an increase of the independent variable will result in an increase of the dependent variable.
e. Determine the least squares estimator for i.e,
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