Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α=0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 30.57 3.29 48.03 7.80 82.67 7.99 91.97 9.20 67.30 7.28 93.60 13.58
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.
Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a
Bill (dollars) Tip (dollars)
30.57 3.29
48.03 7.80
82.67 7.99
91.97 9.20
67.30 7.28
93.60 13.58
The linear correlation coefficient r is ________.
(Round to three decimal places as needed.)
Determine the null and alternative hypotheses.
Ho: ρ(1)____________ ________________
H1: ρ(2)___________ ________________
(Type integers or decimals. Do not round.)
The test statistic is _________.
(Round to two decimal places as needed.)
The P-value is _________.
(Round to three decimal places as needed.)
Because the P-value of the linear correlation coefficient is (3) ___________the significance level, there (4)____________ sufficient evidence to support the claim that there is a linear correlation between bill amounts and tip amounts.
If everyone were to tip with the same percentage, then r = ________ .
(Round to three decimal places as needed.)
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