Question

Aarush started a business 6 months back. It has been noted that his income increases exponentially every month.
(a) Identify the appropriate regression model to illustrate Aarush’s score trend.
(b) Write the formula/equation for the regression model.
(c) Draw a sample chart with dummy data depicting the above discussed regression model.

Hint:

Use exponential regression when data grows by a constant percentage rather than a constant amount.

Answer 1

(a) Since Aarush’s income increases exponentially, the appropriate regression model is the Exponential Regression Model.
This model is used when data shows a constant percentage growth or decay over time.
(b) The general formula for an exponential regression model is:
$Y = ab^X$
Where:
$Y$ = predicted value (income)
$a$ = initial value (income at start)
$b$ = base or growth factor (greater than 1 for growth)
$X$ = independent variable (months)
Example: If Aarush started with \$1000 income and it grows by 20% each month, then
$Y = 1000 \times (1.20)^X$
(c) A sample chart with dummy data can be drawn using months (1 to 6) on the X-axis and income on the Y-axis.
Example dummy data:
Month 1: \$1000
Month 2: \$1200
Month 3: \$1440
Month 4: \$1728
Month 5: \$2074
Month 6: \$2489
This chart will show a rising curve that steepens over time, indicating exponential growth.