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According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:

Month
Average Maximum Monthly Temperature
Jan
48.1
Feb
50.9
Mar
62.4
Apr
67.0
May
76.5
Jun
83.9
Jul
86.8
Aug
88.1
Sep
79.2
Oct
69.9
Nov
59.5
Dec
49.6

Plot the data on a scatter plot. Produce a sine regression model for the data. Round the values for a, b, c, and d to the nearest 0.001. Using the sine regression model predict what the temperature would be given y(30).
a.
58.4 degrees
b.
62.3 degrees
c.
76.8 degrees
d.
86.0 degrees


Please select the best answer from the choices provided

Respuesta :

the average maximum would be C. 76.8 degrees
MrRoyal

The sine regression model is [tex]y =20.077 \sin(0.500x- 1.959) + 67.577[/tex], and the value of y(30) is 76.8 degrees

What is a regression model?

A regression model is used to determine the association and correlation between two variables

Using a graphing calculator, the sine regression model of the dataset is:

[tex]y =20.077 \sin(0.500x- 1.959) + 67.577[/tex]

To calculate y(30), we substitute 30 for x in the equation.

So, we have:

[tex]y =20.077 \sin(0.500 * 30- 1.959) + 67.577[/tex]

Evaluate the product

[tex]y =20.077 \sin(15- 1.959) + 67.577[/tex]

Evaluate the difference

[tex]y =20.077 \sin(13.041) + 67.577[/tex]

Evaluate the sine value

[tex]y =20.077 *0.4570+ 67.577[/tex]

Evaluate the product

[tex]y =9.1752+ 67.577[/tex]

Evaluate the sum

[tex]y =76.7522[/tex]

Approximate

[tex]y \approx 76.8[/tex]

Hence, the sine regression model is [tex]y =20.077 \sin(0.500x- 1.959) + 67.577[/tex], and the value of y(30) is 76.8 degrees

Read more about regression models at:

https://brainly.com/question/17844286

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