We expect a car's highway gas mileage to be related to its city gas mileage. Data for all 1198 vehicles in the government's 2008 Fuel Economy Guide gives the following regression line: highway mpg = 4.62 + (1.109 X city mpg) for predicting highway mileage from city mileage. What is the slope of this line? Give your answer to 3 decimal places. Say in words what the numerical value of the slope tells us. On the average, highway mileage decreases by 1.109 mpg for each additiona
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.
We expect a car's highway gas mileage to be related to its city gas mileage. Data for all 1198 vehicles in the government's 2008 Fuel Economy Guide gives the following regression line: highway mpg = 4.62 + (1.109 X city mpg) for predicting highway mileage from city mileage.
What is the slope of this line? Give your answer to 3 decimal places.
Say in words what the numerical value of the slope tells us.
- On the average, highway mileage decreases by 1.109 mpg for each additional mpg in city mileage.
- On the average, highway mileage increases by 4.62 mpg for each additional mpg in city mileage.
- On the average, highway mileage increases by 1.109 mpg for each additional mpg in city mileage.
What is the intercept? Give your answer in mpg's to 2 decimal places.
Explain why the value of the intercept is not statistically meaningful.
- Because this is the highway mileage for zero city mpg.
- Because this is an average value, calculated from a sample.
- Because this is the highway mileage for slope 0.
Find the predicted highway mileage for a car that gets 16 miles per gallon in the city. Give your answer in mpg to 2 decimal places.
Find the predicted highway mileage for a car that gets 28 miles per gallon in the city. Give your answer in mpg to 2 decimal places.
Draw a graph of the regression line for city mileages between 10 and 50 mpg. (Be sure to show the scales for the x and y axes.) Choose the correct graph.
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