A scientist collected the following data on the speed, in centimeters per second, at which ants ran at the given ambient temperature, in degrees Celsius.† Temperature Speed 25.6 2.62 27.5 3.03 30.3 3.57 30.4 3.56 32.2 4.03 33.0 4.17 33.8 4.32 (a) Find the equation of the regression line, giving the speed S as a function of the temperature t. (Round the regression line parameters to four decimal places.) S(t) = (b) Explain in practical terms the meaning of the slope of the regression line. (Round your answers to four decimal places.) The slope of ____ means that for each increase in temperature of one degree Celsius, the ants run ____ centimeters per second ____ (c) Express, using functional notation, the speed at which the ants run when the ambient temperature is 29 degrees Celsius. S ( ____ ) Estimate that value. (Round your answer to two decimal places.) _____cm/sec (d) The scientist observes the ants running at a speed of 2.46 centimeters per second. What is the ambient temperature? (Round your answer to two 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.
A scientist collected the following data on the speed, in centimeters per second, at which ants ran at the given ambient temperature, in degrees Celsius.†
| Temperature | Speed |
|---|---|
| 25.6 | 2.62 |
| 27.5 | 3.03 |
| 30.3 | 3.57 |
| 30.4 | 3.56 |
| 32.2 | 4.03 |
| 33.0 | 4.17 |
| 33.8 | 4.32 |
(a) Find the equation of the regression line, giving the speed S as a function of the temperature t. (Round the regression line parameters to four decimal places.)
S(t) =
S ( ____ )
_____cm/sec
______ °C
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