The following summary statistics resulted from a study of the relationship between the cost of a barrel of crude oil (x) and the price of a gallon of regular unleaded gasoline (y). n = 12 x 241.1 y 14.34 4,932.8 2 x 17.288 2 y xy 291.55 (1) Compute the sample correlation r and use it to judge the strength of linear relationship between x and y. (2) Obtain the equation of the least squares line, and interpret its slope and intercept. (3) Predict the price of a gallon of regular unleaded gasoline when the cost of a barrel of crude oil is 50.
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.
The following summary statistics resulted from a study of the relationship between the cost of
a barrel of crude oil (x) and the price of a gallon of regular unleaded gasoline (y).
n = 12
x 241.1 y 14.34 4,932.8
2 x 17.288 2 y xy 291.55
(1) Compute the sample
between x and y.
(2) Obtain the equation of the least squares line, and interpret its slope and intercept.
(3) Predict the price of a gallon of regular unleaded gasoline when the cost of a barrel of crude
oil is 50.
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1. The following summary statistics resulted from a study of the relationship between the cost of a barrel of crude oil (x) and the price of a gallon of regular unleaded gasoline (y):
\[
n = 12 \\
\sum x = 241.1 \\
\sum y = 14.34 \\
\sum x^2 = 4,932.8 \\
\sum y^2 = 17.288 \\
\sum xy = 291.55
\]
Tasks:
1. Compute the sample correlation coefficient \( r \) and use it to judge the strength of the linear relationship between \( x \) and \( y \).
2. Obtain the equation of the least squares line, and interpret its slope and intercept.
3. Predict the price of a gallon of regular unleaded gasoline when the cost of a barrel of crude oil is 50.
2. A survey designed to obtain information on \( p \), the proportion of registered voters who are in favor of a constitutional amendment requiring a balanced budget, results in a sample size of \( n = 400 \). Of the 400 voters sampled, 272 are in favor of a constitutional amendment requiring a balanced budget.
Tasks:
1. Give a point estimate of \( p \).
2. Suppose that the standard error for the point estimate is 0.03. Calculate a 95% confidence interval for \( p \) and interpret the confidence interval.
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