$20 $10 Avg Temp $0 10 20 30 40 -$10 -$20 Residual
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Heating After keeping track of his heating expenses for
several winters, a homeowner believes he can estimate
the monthly cost ($) from the average daily Fahrenheit
temperature with the model Cost = 133 - 2.13 Temp.
Here is the residuals plot for his data:a) Interpret the slope of the line in this context.
b) Interpret the y-intercept of the line in this context.
c) During months when the temperature stays around
freezing, would you expect cost predictions based on
this model to be accurate, too low, or too high? Explain.
d) What heating cost does the model predict for a month
that averages 10°?
e) During one of the months on which the model was
based, the temperature did average 10°. What were the
actual heating costs for that month?
f) Should the homeowner use this model? Explain.
g) Would this model be more successful if the
temperature were expressed in degrees Celsius?
Explain.
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