Sinusoidal Regression Model Example

Data:  The table below shows the highest daily temperatures (in degrees Fahrenheit) averaged over the month for the cities of Syracuse, NY; Washington, DC; and Austin, TX.

 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1 2 3 4 5 6 7 8 9 10 11 12 Syracuse, NY 32 34 43 57 69 78 82 80 72 60 48 36 Washington, DC 43 47 56 67 75 84 88 87 80 68 58 47 Austin, TX 62 65 72 80 87 92 96 97 91 82 71 63

The calculator will give the regression equation in the form:
y = a sin (bx + c) + d
where | a | is the amplitude, b is the frequency (where b > 0),
2π/b is the period, | c | / b is the horizontal shift (to the right if c < 0 and to the left if c > 0)
and d is the vertical shift (up if d > 0 and down if d < 0).

Notice that the calculator form is NOT y = A sin (B(x - C)) + D, where B is factored out front.
In the calculator form, the horizontal shift is found by dividing c in the regression equation by b.

 When working with a sinusoidal regression, the calculator will assume that radian mode is enabled.
• If your calculator is set to degree mode, the equation will still be given in terms of radians. While this will be a correct equation, plugged-in values will give incorrect answers. To see correct answers when in degree mode, you will have switch to radian mode (or you can multiply the values of b and c by 180/π).