Question

question 2-3
constructed response: your answer will be scored with the 3-part cer rubric.
the linear regression equation ( y = 4.3x + 126 ) models the relationship between the amount of money ( x ) a company spends on advertising, in dollars, and their revenue ( y ), also in dollars.
what is the rate of change in the regression equation ( y = 4.3x + 126.00 )? explain the meaning of this number.
the rate of change is 4.3. it means that for each additional dollar the company spends on advertising its revenue increases by 4.3 dollars.
a company spends $4,000 on advertising. use the regression equation to predict the companys revenue. use mathematics to justify your prediction.

Explanation:

Step1: Identify the slope in the linear equation

The linear regression equation is \(y = 4.2x+12000\). In the slope - intercept form of a linear equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), for the equation \(y = 4.2x + 12000\), the slope \(m = 4.2\).

Step2: Interpret the slope

The slope \(m = 4.2\) represents the rate of change. In the context of the problem, where \(x\) is the amount of money spent on advertising (in dollars) and \(y\) is the revenue (in dollars), the rate of change means that for every additional dollar the company spends on advertising, the company's revenue increases by \(4.2\) dollars.

Step3: Predict the revenue when \(x = 40000\)

Substitute \(x = 40000\) into the equation \(y=4.2x + 12000\).

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Answer:

The rate of change is \(4.2\). It means that for each additional dollar the company spends on advertising, the company's revenue increases by \(4.2\) dollars. When the company spends \(x = 40000\) dollars on advertising, the predicted revenue \(y = 180000\) dollars.