Question

question
rajani has a part - time job at an ice skating rink selling hot cocoa. she decided to plot the number of hot cocoas she sold relative to the days high temperature and then draw the line of best fit. calculate the residual for the data point that corresponds to 92 hot cocoas sold and a high temperature of 24°f.
(the chart shows a scatter plot with a line of best fit. the x - axis is high temperature (degrees fahrenheit) with values from 4 to 48, and the y - axis is hot cocoas sold with values from 49 to 126. some points on the line of best fit are (0,119), (8,112), (16,105), (24,98), (32,91), (40,84), (48,77))

Explanation:

Step1: Recall Residual Formula

Residual is calculated as \( \text{Residual} = \text{Observed Value} - \text{Predicted Value} \).

Step2: Identify Observed and Predicted Values

Observed value (hot cocoas sold) when temperature is \( 24^\circ\text{F} \) is \( 92 \). From the line of best fit, at \( x = 24 \), the predicted value (from the point \( (24, 98) \) on the line) is \( 98 \).

Step3: Calculate Residual

Substitute into the formula: \( \text{Residual} = 92 - 98 = -6 \).

Answer:

\(-6\)