part of my egents packet

Question

Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from co

ee sales.

Data from nine days this past fall are shown in the table below.

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9

High Temperature, t 54 50 62 67 70 58 52 46 48

Coffee Sales, f(t) $2900 $3080 $2500 $2380 $2200 $2700 $3000 $3620 $3720

State the linear regression function, f(t), that estimates the day's coffee sales with a high temperature of t. Round all values to the nearest integer.

State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong linear relationship

between the variables? Explain your reasoning.

Answer 1

I'll assume that you are using a TI graphing calculator in your class.

Enter the data for temperature in List 1.

Enter the data for coffee sales in List 2.

Go to Stat/Tests. Scroll all the way down to LinRegTTest. For Xlist (Independent or predictor variable) choose L1 (temperature); For YList (dependent or response variable) choose List2 (Coffee sales).

Calculate.

Our model will be of the form f(t) = a+bt, where t is temperature.

(We are not asked to run a t-test, so we don't need the t-score or the p-value, we are looking for a and b. Scroll down a bit. The values for a and b are there in the output.)

f(t) = 6183-58t

So for a day when expected temperatures are 55 degrees f(55)=6183-58(55)= 2948 or $2948

The correlatin coefficient, r, is also there in the output. Scroll down.

r = -0.944

Recall r is a number whose absolute value is between 0 and 1; the closer to 1, the stronger the correlation.

This is a strong negative correlation, or linear relationship.

Hope that helps!

By the way we could have used Stat/Calc/LinReg, to find the regression function, but we also needed the correlation coefficient, r. That's why I used the LinRegTTest instead.

Answer 2

By using Excel in Data Analysis, the linear regression is:

f(t) = -58.26t + 6182.20, where t is high temperature (in degrees) and f(t) is the amount of sales for coffee.

Each time you raise the temperature by 1 degree, then coffee sales will decrease by $58.26.

The estimated equation will be f(t) = -58t + 6182.

The correlation between higher temperature and coffee sales is about -0.9441. This is a strong, negative correlation. Research shows that most people want their coffee hot when cooler temperatures exist. For example, hot coffee is better during the winter as opposed to during the summer.