The following table gives information on the limited tread warranties (in thousands of miles) and the prices ($) of twelve randomly selected tires at a national tire retailer as of July 2020.\ Warranty 60 70 75 50 80 55 65 65 70 65 60 65 Price per tire 95 135 94 90 121 70 140 80 92 125 160 155 a) Find the correlation coefficient and interpret your result. b) Draw a scatter diagram for the above data and make a comment. c) Find the estimated least-squares regression line.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The following table gives information on the limited tread warranties (in thousands of miles) and the prices ($) of twelve randomly selected tires at a national tire retailer as of July 2020.\
|
Warranty |
60 |
70 |
75 |
50 |
80 |
55 |
65 |
65 |
70 |
65 |
60 |
65 |
|
Price per tire |
95 |
135 |
94 |
90 |
121 |
70 |
140 |
80 |
92 |
125 |
160 |
155 |
a) Find the
b) Draw a
c) Find the estimated least-squares regression line.
d) Interpret the estimated slope and intercept value.
e) Test at a 5% significance level whether the slope in the regression model is positive?
f) Suppose that each value of price per tire given in the table is increased by 10 and the warranty values remain unchanged. Would you expect sample correlation (r) to increase, decrease, or remain the same? How do you expect the least-squares regression line to change?
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