Question

A coffee shop takes daily data on the high temperature for the day in degrees F, and the number of cups of hot chocolate sold. They construct a scatterplot and examine the linear relationship.The least squares regression line equation is:
y=76.42-1.38x

1.Using the slope value, describe the relationship in context. 2.Can this line equation be used to make a prediction for number of cups of hot chocolate sold when it's 60 degrees F outside? Explain.3.The coffee shop took similar data on coffee consumption and temperature, and arrived at an estimated regression equation:
y=105.0-1.67x

A t-test on the slop results in a p-value=0.156. Explain how you would interpret the slope of the regression line.

Answer 1

y =76.42-1.38x

x: high temperature for the day in degrees F (Also the independent variable)

y: the number of cups of hot chocolate sold (The dependent variable)

Let us now go ahead with solving the questions-

1) Slope = 76.42

Interpretation: Independent of the day-high temperature/ assuming that the day high is 0, the shop will be able to sell 76 cups of hot chocolate per day

2) Yes! Put x=60

We have y = 76.42 - 1.38*60

The value turns out to be negative though but we can predict

3) y=105.0-1.67x

x: temperature

y: coffee consumption

Interpreting slope: Slope= 105

p-value is 0.156

p-value > alpha (at 95% CI)

It indicates that the result is not statistically significant

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