Question

let ( y ) represent the profit (or loss) for a certain company ( x ) years after 1970. based on the data shown below, a statistician calculates a linear model ( y = 1.83x + 10.69 ).
\begin{tabular}{|c|c|} hline x & y \\ hline 1 & 11.24 \\ hline 2 & 16.38 \\ hline 3 & 15.42 \\ hline 4 & 18.46 \\ hline 5 & 19.1 \\ hline 6 & 20.14 \\ hline 7 & 25.28 \\ hline 8 & 27.12 \\ hline 9 & 25.86 \\ hline 10 & 28.5 \\ hline end{tabular}
use the model to estimate the profit in 1974
( y = )
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Explanation:

Step1: Determine X for 1974

1974 is 1974 - 1970 = 4 years after 1970, so \( X = 4 \).

Step2: Substitute X into the model

The linear model is \( Y = 1.83X + 10.69 \). Substitute \( X = 4 \):
\( Y = 1.83\times4 + 10.69 \)

Step3: Calculate the value

First, calculate \( 1.83\times4 = 7.32 \). Then, add 10.69: \( 7.32 + 10.69 = 18.01 \).

Answer:

18.01