Olivia would like to compare the climate of Johannesburg to

Olivia would like to compare the climate of Johannesburg to the climates of the following 3 cities already graphed below

She collects data for the month of the year m and the average daily high temperature H in degrees celcius. As before , m=0 represents the first day of January and m=11 represents the first day of December.

A) Using your graphing calculator to perform a sinusoidal regression on the data. Write the function in the form:

a sin(bm + c) + d.. Round off a,b,c, and d to 4 decimal places.

B) What if Johannesburg\'s function had the same midline as Havana\'s and its climate were as variable as Hong Kongs? Rewrite the function for Johannesburg to account for these new paramenters, and complete the missing values in the table. Give the temperatures to the nearest tenth of a degree.

H(m)_____________________

Solution

To solve for the values of a,b,c,d

We follow the following steps in Excel

Step1. Define the data as just described.

Step2. Define the model to be H =a*sin(bm + c) + d

Step3. Define S to be the sum of squared differences between the data and the model

Step4. Use SOLVER to minimize S by varying a,b,c,d

On solving you get the following values :

a = 4.38

b = 0.66

c = 1.181

d = 21.08

For the second part,

The midline of Johanesburg and Havana are the same. The midline is what IU presume to be the average value about which the function oscillates. This is obtained when sin (bm+c) = 0

Thus, it is the \'d\' value.

Johanesburg function will have the d = 21.08. The other values that induce the variability are a,b,c which would be same as for hong kong\'s. Thus, you need to know the parameters of hong kong to determine the function for johanesburg.

Once you get that, plug in different values of m to fill the table.

Ask if you have any doubts.