A statistical program is recommended. Consider the following data for two variables, x and y. x 22 24 26 30 35 40 y 12 22 34 36 41 37 (d) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to one decimal place and b1 to two decimal places and b2 to four decimal places.) ŷ = −175+12.63x−.1837x2 Use the results from part (d) to test for a significant relationship between x, x2, and y. Use α = 0.05. Is the relationship between x, x2, and y significant? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.)
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.
| x | 22 | 24 | 26 | 30 | 35 | 40 |
|---|---|---|---|---|---|---|
| y | 12 | 22 | 34 | 36 | 41 | 37 |
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