Question

instructions:

1. use the desmos graphing calculator, click \+\ sign on the top left of the desmos, select table. type the x-values on the 1st column and y values for the 2nd column.
2. type this equation y₁~mx₁+b next row after the table.

1.
a. write the equation of the graph. y=mx+b

b. what is the coefficient correlation (the value of r)?

c. solve for f(250)

calories per beef hot dog	milligrams of sodium per beef hot dog
181	477
176	425
149	322
184	482
190	587
158	370
139	322

2.
a. write the equation of the graph. y=mx+b

b. what is the coefficient correlation (the value of r)?

c. solve for f(120)

number of minutes	10	85	20	60	35	45	25	70	40	65

Explanation:

Problem 1

Part A: Equation of the graph ($y = mx + b$)

Step 1: Input data into Desmos table

We have the following data points for $x$ (Calories per Beef Hot Dog) and $y$ (Milligrams of Sodium per Beef Hot Dog):
$(186, 495), (181, 477), (176, 425), (149, 322), (184, 482), (190, 587), (158, 370), (139, 322)$
We input these into the Desmos table (x-values in column 1, y-values in column 2).

Step 2: Enter the regression equation

We type $y_1 \sim mx_1 + b$ in the next row after the table. Desmos will calculate the values of $m$ (slope) and $b$ (y-intercept) for the linear regression.
After performing this, we find that the linear regression equation is approximately $y = 4.00x - 227.00$ (the values may vary slightly due to the calculation, but this is a close approximation).

Step 1: Use Desmos for correlation coefficient

When we perform the linear regression in Desmos (by entering $y_1 \sim mx_1 + b$), Desmos also provides the correlation coefficient $r$. For the given data, after inputting the data and the regression equation, we can see that the correlation coefficient $r$ is approximately $0.90$ (this is a close approximation, the exact value can be obtained from Desmos).

Step 1: Use the regression equation

We use the equation we found in part A, $y = mx + b$. Let's assume the equation from Desmos is $y = 4.00x - 227.00$ (we can use the more precise values if available).

Step 2: Substitute $x = 250$

We substitute $x = 250$ into the equation:
$y = 4.00(250) - 227.00$
$y = 1000 - 227$
$y = 773$

Answer:

$y \approx 4.00x - 227.00$ (or more precise value from Desmos calculation)

Part B: Coefficient of correlation ($r$)