Forecasting Revenue with Linear Trend Model

ABC Corp. has been tracking its quarterly revenue over the past three years and is interested in forecasting future revenue. The company determines that a linear trend model is appropriate for its revenue data. The quarterly revenue data (in millions) for the last twelve quarters is as follows: 12, 15, 13, 17, 18, 20, 22, 25, 28, 29, 30, 35. The company uses the equation of a trend line, given by:

$$ Y_t = a + bt $$

where:

$$ Y_t $$ is the revenue in quarter t,

$$ a $$ is the intercept,

$$ b $$ is the slope (the estimated increase in revenue per quarter),

and $$ t $$ is the time index (1 for the first quarter, 2 for the second, etc.). Using the least squares method, what is the forecast for revenue in the 13th quarter if the slope $$ b $$ is found to be 1.5 and the intercept $$ a $$ is calculated to be 10?