Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possble to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F). 20.4 16.2 15.5 19.8 15.3 73.2 18.1 14.7 69.7 х 78.8 17.1 95.3 86.1 75.2 82.0 15.4 16.2 15.0 16.0 80.6 82.6 14.4 17.0 83.5 Complete parts (a) through (e), given Ex = 248.3, y = 1205, Ex? = 4153.89, Ey = 97,496.94, Exy = 20,102.32, and r 0.892. х 69.4 17.2 83.3 79.6 76.3
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.
(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
| r2 = | |
| explained | % |
| unexplained | % |
(f) What is the predicted temperature when x = 17.4 chirps per second? (Round your answer to two decimal places.)
°F
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