Run a regression analysis on the following bivariate set of data with y as the response variable. x y 48.3 56.5 47.8 58.1 50.7 57.2 48.1 56.9 47.3 56.4 44.6 54.6 47.1 56.1 48.6 57.2 50.3 58.2 46.8 56.3 49.8 57 51.7 57.9
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 | y |
|---|---|
| 48.3 | 56.5 |
| 47.8 | 58.1 |
| 50.7 | 57.2 |
| 48.1 | 56.9 |
| 47.3 | 56.4 |
| 44.6 | 54.6 |
| 47.1 | 56.1 |
| 48.6 | 57.2 |
| 50.3 | 58.2 |
| 46.8 | 56.3 |
| 49.8 | 57 |
| 51.7 | 57.9 |
r =
What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)
r² = %
Based on the data, calculate the regression line (each value to three decimal places)
y = blank x + blank
Predict what value (on average) for the response variable will be obtained from a value of 49.5 as the explanatory variable. Use a significance level of α=0.05 to assess the strength of the
What is the predicted response value? (Report answer accurate to one decimal place.)
y =
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