K Question 18 of 18 Question Suppose Joy, an owner of a frozen yogurt Store, wan

Question

K Question 18 of 18 Question Suppose Joy, an owner of a frozen yogurt Store, wants to understand the relationship between temperature and frozen yogurt sales. She records the highest daily temperature, in degrees Celsius (°C), and the daily amount of frozen yogurt sold, in kg, for 32 randomly selected days. The least-squares regression equation for her data is where represents the highest daily temperature C), and y represents the predicted amount of frozen yogurt sold (kg) on a day when the highest daily temperature is x. Summary statistics for the model are provided in the table. Standard error Standard error Sample size of mean response of prediction SE SE 6.37251 1.31130 32 Assuming that the requirements for a least-squares regression model have been met compute the predicted amount of frozen yogurt sold in a day when the temperature is 28 C. Provide your answer precise to three decimal places. Avoid rounding until the final step. kg

Explanation / Answer

Answer to the question)

The predicted amount of frozen yogurt is :

Y^ = 5.57125 * 28 + 165.1723

Y^ = 321.1673

.

The T critical value is based on df = n-2

we got n = 32

df = 30

confidence level (c) = 0.90

T critical = 1.697 ................[referred to T table for the T critical value , c=0.90 & df = 30]

.

The value of confidence interval is:

Y^ - T*SE, Y^ + T*SE

We got

Y^ = 321.1673

T = 1.697

SE = 6.37251

.

on plugging these values we get:

321.1673 - 1.697 * 6.3725 , 321.1673 + 1.697 * 6.3725

310.3532 , 331.9814

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