Kace does not have a very good credit rating. In January of 2021, he found a lending institution that was willing to loan him $200,000 for 15 years at a higher than normal interest rate of 6% because of his poor credit rating. Examine the table of decreasing loan balances over the 15-year period. Use regression to determine a curve of best fit for this data.

1	$11,769.23	$8,483.33	$191,516.67
2	$11,246.00	$9,006.57	$182,510.10
3	$10,690.49	$9,562.07	$172,948.02
4	$10,100.72	$10,151.84	$162,796.18
5	$9,474.58	$10,777.98	$152,018.20
6	$8,809.82	$11,442.75	$140,575.45
7	$8,104.05	$12,148.51	$128,426.94
8	$7,354.76	$12,897.80	$115,529.13
9	$6,559.25	$13,693.31	$101,835.82
10	$5,714.68	$14,537.89	$87,297.94
11	$4,818.01	$15,434.55	$71,863.38
12	$3,866.04	$16,386.52	$55,476.86
13	$2,855.36	$17,397.21	$38,079.66
14	$1,782.34	$18,470.23	$19,609.43
15	$643.13	$19,609.43	$-0.00

The curve of best fit for the loan balance data follows a quadratic equation of the form:

\[
y = -7102.00x + (-403.28)x^2 + 198186.01
\]

where:
- $ y $ is the loan balance,
- $ x $ is the year (1 to 15),
- 198186.01 is the intercept, representing the starting balance,
- $-7102.00$ and $-403.28$ are the coefficients that model the decreasing balance over time.

Would you like further details or explanations? Here are five related questions to explore:

1. How do the coefficients affect the shape of the curve?
2. How can this regression model be used to predict future balances?
3. What is the difference between linear and quadratic regression in this context?
4. How would the balance curve change with a lower interest rate?
5. Can we calculate the total interest paid over the loan period?

**Tip:** Quadratic regression is commonly used when a relationship starts fast and then slows, as is the case with loan repayments.

Kace does not have a very good credit rating. In January of 2021, he found a lending institution that was willing to loan him $200,000 for 15 years at a higher than normal interest rate of 6% because of his poor credit rating. Examine the table of decreasing loan balances over the 15-year period. Use regression to determine a curve of best fit for this data.

Explore how to use quadratic regression to find a curve of best fit for a 15-year loan repayment plan with a 6% interest rate. The initial loan amount is $200,000, and the data shows the decreasing loan balance each year. Learn about key mathematical concepts such as regression analysis and quadratic equations. Suitable for Grades 10-12.

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