For the data below, draw a scatter plot on each graph provided. Then use your graphing calculator to find the line of best fit and the correlation coefficient. Round all numbers to three decimal places. Line of Best Fit: Correlation Coefficient: What conclusions can you draw about the relationship between calories and fat? Line of Best Fit: Correlation Coefficient: What conclusions can you draw about the relationship between calories and sodium? If you are asked to report your opinion on which relationship is stronger: calories and fat, or calories and sodium, what would your opinion be? Why?
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.
For the data below, draw a
Line of Best Fit:
Correlation Coefficient:
What conclusions can you draw about the relationship between calories and fat?
Line of Best Fit:
Correlation Coefficient:
What conclusions can you draw about the relationship between calories and sodium?
If you are asked to report your opinion on which relationship is stronger: calories and fat, or calories and sodium, what would your opinion be? Why?
Strength of relationship between variables using correlation:
- If the value of correlation is between 0.7 to 1 or -1 to -0.7 the relation between variables is strong.
- If the value of correlation is between 0.5 to 0.69 or -0.69 to -0.5 the relation between variables is moderate.
- If the value of correlation is between 0 to 0.49 or -0.49 to 0 the relation between variables is weak.
For calories and fat:
Use Ti calculator to find the line of best fit as follows:
- Select STAT > Edit > Enter the values of Fat as L1, values of calories as L2.
- Click 2 nd button; then '0' number key, and then choose DiagnosticOn. Click Enter.
- Select STAT > CALC > LinReg(a+bx).
- Click Enter.
Output:
From the output, the line of best fit is and correlation coefficient is 0.500.
The correlation between calories and fat is 0.5, there is moderate relationship between the variables and the value is positive indicating that there is moderate positive relationship between the variables.
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