Listed below are sixes (in thousands of square feet) and...

Listed below are sixes (in thousands of square feet) and revenue (in millions of dollars) from casinos in Atlantic City (based on data from the New York Times). Is there sufficient evidence to conclude that there is a linear correlation between size and revenue of casinos? $$\begin{array}{l|ccccccc}\text { Size } & 160 & 227 & 140 & 144 & 161 & 147 & 141 \\\hline \text { Revenue } & 189 & 157 & 140 & 127 & 123 & 106 & 101\end{array}$$

Listed below are sixes (in thousands of square feet) and revenue (in millions of dollars) from casinos in Atlantic City (based on data from the New York Times). Is there sufficient evidence to conclude that there is a linear correlation between size and revenue of casinos?
$$\begin{array}{l|ccccccc}\text { Size } & 160 & 227 & 140 & 144 & 161 & 147 & 141 \\\hline \text { Revenue } & 189 & 157 & 140 & 127 & 123 & 106 & 101\end{array}$$

Key Concepts

p-value

The p-value is a probability metric used in hypothesis testing to determine the strength of the evidence against the null hypothesis. A small p-value indicates that the observed correlation is unlikely to have occurred by chance, thus providing support for the existence of a statistically significant linear relationship between the variables.

Hypothesis Testing for Correlation

Hypothesis testing for correlation involves evaluating whether the observed linear relationship, as measured by the Pearson correlation coefficient, is statistically significantly different from zero. The null hypothesis typically states that there is no linear association between the variables, while the alternative hypothesis asserts that a linear correlation exists.

Linear Correlation

Linear correlation measures the strength and direction of a straight-line relationship between two continuous variables. It is a fundamental concept in statistics that helps determine how one variable may predict or be associated with changes in another, assuming the association is linear.

Pearson Correlation Coefficient

The Pearson correlation coefficient is a numerical measure ranging from -1 to 1 that quantifies the degree of the linear relationship between two variables. A value close to 1 indicates a strong positive linear relationship, a value near -1 indicates a strong negative linear relationship, and a value near 0 suggests little to no linear relationship.

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