Question

Create a linear regression equation that can be used to model the amount of money in the account (the balance), y, based on the time (in weeks), x. Round all values to the nearest hundredth.
Use the model to approximate the amount in the account after 15 weeks. Round to the nearest hundredth.
Use the model to approximate how long it would take to have $50.00 in the account.

Answer 1

The regression equation is $\^y = 1.56\^x + 1.29$, and it will take 31 weeks to have $50.00

(a) The linear regression equation

To do this, we make use of a graphing calculator;

From the graphing calculator, we have the following calculation summary:

• The sum of X = 45
• The sum of Y = 83
• Mean X = 4.5
• Mean Y = 8.3
• Sum of squares (SSX) = 82.5
• Sum of products (SP) = 128.5

The regression equation is then represented as:

$\^y = b\^x + a$

Where:

$b = \frac{SP}{SSX}$ and $a = M_Y - bM_X$

So, we have:

$b = \frac{128.5}{82.5}$

$b = 1.55758$

Approximate

$b = 1.56$

$a= 8.3 - (1.56 \times 4.5)$

$a= 1.29091$

Approximate

$a= 1.29$

This means that, the regression equation is $\^y = 1.56\^x + 1.29$

(b) Predict the time to have $50.00

This means that:

$\^y = 50$

So, we have:

$50 = 1.56\^x + 1.29$

Subtract 1.29 from both sides

$48.71 = 1.56\^x$

Divide both sides by 1.56

$31.22 = \^x$

Rewrite as:

$\^x = 31.22$

Approximate

$\^x = 31$

Hence, it will take 31 weeks to have $50.00

Read more about linear regression models at:

brainly.com/question/14585820