An economist wanted to analyze the relationship between the speed of a car (x) and it's gas mileage (y). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These date are shown below. speed (x) -> 25 35 45 50 60 65 70 gas mileage (y) -> 40 35 37 33 30 25 20 correlation coefficient is : The equation of regression line is: estimate the gas mileage of a car traveling 70 mph. the coefficient of determination (R-square): test the significance of the correleation coefficient using a= 0.05 and the claim p<0 •H0: p> or equal to 0 •Ha: p<0 •a=0.05 •n=7 •df= critical value(s) from t distribution table using a=0.05 is : type of test (left, right, two tailed) standardized test statistic: decision (reject ho/dont): conclusion: we conclude that
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.
An economist wanted to analyze the relationship between the speed of a car (x) and it's gas mileage (y). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These date are shown below.
speed (x) -> 25 35 45 50 60 65 70
gas mileage (y) -> 40 35 37 33 30 25 20
The equation of regression line is:
estimate the gas mileage of a car traveling 70 mph.
the coefficient of determination (R-square):
test the significance of the correleation coefficient using a= 0.05 and the claim p<0
•H0: p> or equal to 0
•Ha: p<0
•a=0.05
•n=7
•df=
critical value(s) from t distribution table using a=0.05 is :
type of test (left, right, two tailed)
standardized test statistic:
decision (reject ho/dont):
conclusion: we conclude that
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