What values did you select in excel? Can you please clarify? Five observations taken for two variables follow. xi 4 6 11 3 16 yi 50 50 40 60 20 (a) Develop a scatter diagram with x on the horizontal axis.
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.
|
xi
|
4 | 6 | 11 | 3 | 16 |
|---|---|---|---|---|---|
|
yi
|
50 | 50 | 40 | 60 | 20 |
- The horizontal axis is labeled: x, and
ranges from 0 to 20. - The vertical axis is labeled: y, and ranges from 0 to 80.
- The leftmost point on the plot is at about (3 , 48).
- Moving right, second point is below and to the right of the first point.
- The third point is above and to the right of the second point.
- The fourth point is below and to the right of the third point.
- The fifth point is below and to the right of the fourth point.
a negative
relationship between the two variables.
Expert Answer
(a) Scatter diagram:
Step-by-step procedure for scatter diagram using EXCEL is given below:
- Click on Insert> Charts>Scatter>Scatter with only Markers
- Under Layout> Chart title>Above chart> type Scatter plot
- Under Layout> Axis titles>Primary Horizontal Axis title>Title Below Axis> type x
- Under Layout> Axis titles>Primary Vertical Axis title>Rotated Title> type y
The output for scatter plot is given below:
- The horizontal axis is labeled: x, and ranges from 0 to 20.
- Moving right, second point is below and to the right of the first point.
- The fourth point is below and to the right of the third point.
- The fifth point is below and to the right of the fourth point.
(b) Relationship between the two variables using scatter plot:
The scatter diagram indicates that there is a negative relationship between the two variables.
(c) Sample covariance: What values did you select in excel?
The sample covariance can be calculated using EXCEL
Thus, the sample covariance is -80.
Based on the sample covariance, there is a negative linear relationship between the two variables, but the strength of this relationship cannot be determined based on the sample covariance.
(d) Correlation coefficient:
The correlation coefficient can be calculated using EXCEL function "=CORREL (select array of values)" as follows: What values did you select in excel?
Thus, the correlation coefficient is -0.971.
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