Use the data in the table, which shows the average annual salaries (both Apply what you have learned in the previous in thousands of dollars) for public school principals and teachers in the U.S. for 11 years. tab to complete this graded lab questions. Principals x Teachers y 43.7 1. Repeat the steps from tab #1 using this data to construct a scatter plot graph and 77.8 calculate the correlation coefficient R. (Recall the correlation coefficient is R and not R2) 78.4 43.8 80.8 45.0 R= 80.5 45.6 45.9 2. Does the R value represent a positive, negative or no correlation between the 81.5 salaries of the teachers and principals? As teacher salaries increase, what happens to prinicipal salaries? 84.8 48.2 87.7 49.3 91.6 51.3 3. Write the equation of the regression line for the data below. 93.6 52.9 95.7 95.7 54.4 54.2 The equation is y= 4. Use the regression equation that you found in exercise #3 to predict the average annual salary of public school classroom teachers when the average annual salary of public school principals is $139,723. Show your work in the cells to the right. (Be careful when entering the x-value in the equation. The table shows numbers that have been adjusted in terms of the thousands. Example: if the salary is $82,500, then use x= 82.5) The predicted salary for teachers is _5 when the principal makes $139,723.
Use the data in the table, which shows the average annual salaries (both Apply what you have learned in the previous in thousands of dollars) for public school principals and teachers in the U.S. for 11 years. tab to complete this graded lab questions. Principals x Teachers y 43.7 1. Repeat the steps from tab #1 using this data to construct a scatter plot graph and 77.8 calculate the correlation coefficient R. (Recall the correlation coefficient is R and not R2) 78.4 43.8 80.8 45.0 R= 80.5 45.6 45.9 2. Does the R value represent a positive, negative or no correlation between the 81.5 salaries of the teachers and principals? As teacher salaries increase, what happens to prinicipal salaries? 84.8 48.2 87.7 49.3 91.6 51.3 3. Write the equation of the regression line for the data below. 93.6 52.9 95.7 95.7 54.4 54.2 The equation is y= 4. Use the regression equation that you found in exercise #3 to predict the average annual salary of public school classroom teachers when the average annual salary of public school principals is $139,723. Show your work in the cells to the right. (Be careful when entering the x-value in the equation. The table shows numbers that have been adjusted in terms of the thousands. Example: if the salary is $82,500, then use x= 82.5) The predicted salary for teachers is _5 when the principal makes $139,723.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
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Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Transcribed Image Text:Use the data in the table, which shows the average annual salaries (both
Apply what you have learned in the previous
2
tab to complete this graded lab questions.
in thousands of dollars) for public school principals and teachers in the
U.S. for 11 years.
3
4
R
Principals x
Teachers y
0.9975
1. Repeat the steps from tab #1 using this data to construct a scatter plot graph and
calculate the correlation coefficient R. (Recall the correlation coefficient is R and not R2)
5
77.8
43.7
6
78.4
43.8
Teachers y
R=
7
80.8
80.5
81.5
45.0
45.6
8
2. Does the R value represent a positive, negative or no correlation between the
45.9
9
60.0
84.8
87.7
salaries of the teachers and principals? As teacher salaries increase, what happens to
prinicipal salaries?
48.2
y-0.5873x - 2.0507
R=0.995
10
49.3
11
91.6
51.3
50.0
93.6
52.9
54.4
3. Write the equation of the regression line for the data below.
The equation is y=
12
95.7
95.7
13
54.2
40.0
14
4. Use the regression equation that you found in exercise #3 to predict the average
annual salary of public school classroom teachers when the average annual salary of
public school principals is $139,723. Show your work in the cells to the right.
15
30.0
16
17
(Be careful when entering the x-value in the equation. The table shows numbers that
20.0
18
have been adjusted in terms of the thousands. Example: if the salary is $82,500, then
use x- 82.5)
19
The predicted salary for teachers is _$ when the principal makes $139,723.
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80.0
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