Annual high temperatures in a certain location have been tracked for several years. Let XX represent the number of years after 2000 and YY the high temperature. Based on the data shown below, calculate the linear regression equation using technology (each constant to 2 decimal places). x y 1 33.05 2 32 3 31.55 4 34 5 32.85 6 36.9 7 37.05 8 36.2 9 39.25 10 38.1 11 40.25 The equation is ˆy = x + Interpret the slope For each additional year, the annual high temperature will increase by 30.54 degrees on average. For each additional 0.84 years, the annual high temperature will increase by 1 degree on average. For each additional year, the annual high temperature will increase by 0.84 degrees on average. For each additional 30.54 years, the annual high temperature will increase by 1 degree on average. Interpret the y-intercept In 2000, the temperature was about 30.54. In 2001, the temperature was about 0.84. It does not make sense to interpret the intercept in this scenario. In 2011, the temperature was about 40.25. In 2001, the temperature was about 30.54.
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.
Annual high temperatures in a certain location have been tracked for several years. Let XX represent the number of years after 2000 and YY the high temperature. Based on the data shown below, calculate the linear regression equation using technology (each constant to 2 decimal places).
| x | y |
|---|---|
| 1 | 33.05 |
| 2 | 32 |
| 3 | 31.55 |
| 4 | 34 |
| 5 | 32.85 |
| 6 | 36.9 |
| 7 | 37.05 |
| 8 | 36.2 |
| 9 | 39.25 |
| 10 | 38.1 |
| 11 | 40.25 |
The equation is ˆy = x +
Interpret the slope
- For each additional year, the annual high temperature will increase by 30.54 degrees on average.
- For each additional 0.84 years, the annual high temperature will increase by 1 degree on average.
- For each additional year, the annual high temperature will increase by 0.84 degrees on average.
- For each additional 30.54 years, the annual high temperature will increase by 1 degree on average.
Interpret the y-intercept
- In 2000, the temperature was about 30.54.
- In 2001, the temperature was about 0.84.
- It does not make sense to interpret the intercept in this scenario.
- In 2011, the temperature was about 40.25.
- In 2001, the temperature was about 30.54.
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