Question

the owner of an ice cream stand kept track of the number of ice cream cones that were sold each day of the first week in june. she compared the ice cream sales to the average daily temperature. the data are shown in the table below. state the linear regression equation for these data, rounding all values to the nearest hundredth. state the correlation coefficient, to the nearest hundredth, for the line of best fit for these data. state what this correlation coefficient indicates about the linear fit of the data.

Explanation:

Step1: Input data into calculator

Use a graphing calculator or statistical software. Enter the \(x\)-values (average daily temp: \(72,75,81,78,77,76,80\)) and \(y\)-values (daily ice - cream cone sales: \(126,183,263,229,200,185,249\)).

Step2: Calculate linear regression equation

On a TI - 84 Plus (or similar), go to STAT → CALC → LinReg(ax + b). The calculator will output \(a\) (slope) and \(b\) (y - intercept).

$$
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$$

The linear regression equation is \(y = 10.44x-621.52\).

Step3: Calculate correlation coefficient

From the LinReg(ax + b) calculation, the correlation coefficient \(r\approx0.97\) (to the nearest hundredth).

Step4: Interpret correlation coefficient

The correlation coefficient \(r = 0.97\). Since \(r\) is close to \(1\) (\(0.97\gt0.7\) which is a common threshold for a strong linear relationship), it indicates a strong positive linear relationship between the average daily temperature and the number of ice - cream cones sold.

Answer:

• Linear regression equation: \(y = 10.44x - 621.52\)
• Correlation coefficient: \(r\approx0.97\)
• Interpretation: A strong positive linear relationship between average daily temperature and ice - cream cone sales.