Which of the following is/are true? (A) In reference to question (18), it would be appropriate to approximate the mean mileage when the car is using 85% ethanol (B) In reference to question (18), a 95% confidence interval for β1 is (−0.375, −0.125) (C) If two variables are correlated, then one must cause the other (D) βˆ = Cov(x,y) (think carefully on this one) 1 s2x
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.
18. Because ethanol contains less energy than gasoline, a researcher wants to determine if the mileage of a car (y) is affected by the percent ethanol in the gasoline (x). The true population regression line relating the mean mileage y for a given ethanol content x (in percent) is μy|x = β0 + β1x. In a controlled environment, the mileage of a car is recorded when refueled 7 times using between 0% and 10% ethanol. The least squares regression line was found to be yˆ = βˆ0 + βˆ1x = 32.96 − 0.250x. We wish to test H0 : β1 = 0 versus Ha : β1 < 0 at the α = 0.05 significance level (i.e. we want to determine if the addition of ethanol significantly decreases mean gas mileage). What is the p−value for this test? What is your conclusion? Note: s?e(βˆ1) = 0.0485.
Which of the following is/are true?
(A) In reference to question (18), it would be appropriate to approximate the mean mileage when the car is using 85% ethanol
(B) In reference to question (18), a 95% confidence interval for β1 is (−0.375, −0.125)
(C) If two variables are
(D) βˆ = Cov(x,y) (think carefully on this one) 1 s2x
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