Correlation

A correlation coefficient is calculated as $\displaystyle r = -0.89$.
Interpret this value.

A correlation coefficient is calculated as $\displaystyle r = 0.12$.
Interpret this value.

State the range of possible values of a correlation coefficient, and state what $\displaystyle r = 1$ would mean.

A study finds a strong positive correlation $\displaystyle (r = 0.94)$ between daily ice cream sales and the number of sunburn cases.
A newspaper claims that eating ice cream causes sunburn.
Explain why this conclusion is not valid.

Explain what is meant by a confounding variable.

A scatterplot shows points lying close to a straight line sloping downwards.
State what this suggests about the correlation coefficient.

Statistical software reports a sample correlation of $\displaystyle r = 0.78$ between hours of revision and exam mark.
Interpret this in the context of the study.

You must refer to the spreadsheet file 'Q5 Coffee.csv' for the data, and the word file 'Q5 Coffee Answers.docx' when answering this question.
You must complete parts (a), (b) (i), and (c) (i) using appropriate statistical software.
You must include all output from statistical software, and your answers in the word processing file 'Q5 Coffee answers.docx'.

A specialist coffee shop sells 22 different drinks. For each drink the following data are provided: carbohydrate content (grams), number of calories (kCals). The number of calories is dependent on the carbohydrate content of the drink.

(a) Construct a scatter plot of number of calories on carbohydrate content.

(b)(i) Find the correlation coefficient between number of calories and carbohydrate content.

(b)(ii) Interpret the correlation coefficient.

(c)(i) Find the equation of the regression line of number of calories on carbohydrate content.

(c)(ii) Interpret the slope and intercept parameters.

(d) Estimate the number of calories in a drink which has 59 g of carbohydrate.