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The given equation is the best line that approximates the linear
relationship between the midterm score and the score in the final exam.
- AJ's residual is 0.3, which is not among the given options, therefore, the correct option is. <u>E. None of these</u>.
Reasons:
The given linear regression line equation is; = 25.5 + 0.82·
Where;
= Final exam score;
= The midterm score;
AJ score in the first test, = 90
AJ's actual score in the exam = 99
Required:
The value of AJ's residual
Solution:
By using the regression line equation, we have;
The predicted exam score, = 25.5 + 0.82 × 90 = 99.3
- The residual score = Predicted score - Actual score
∴ AJ's residual = 99.3 - 99 = 0.3
AJ's residual = 0.3
Therefore, the correct option is option E;
- <u>E. None of these</u>
Learn more about regression line equation here:
The ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
<h3>What is a mathematical model?</h3>A mathematical model is the model which is used to explain the any system, the effect of the components by study and estimate the functions of systems.
Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z.
The demand for Model Z depends on the gasoline price (q) because customers tend to purchase an electronic vehicle as a substitute for vehicles that run on gasoline when the gasoline price increases.
The demand for Model Z is estimated as
Here, <em>p</em> is the price of Model Z.
Consider the following two statements:
- 1. When the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X.
- 2. When the average gasoline price q increases by $1, the demand at the revenue-maximizing price (i.e., D(p*)) increases by a factor of Y.
Put the value of demand at the revenue-maximizing price as,
Thus, the ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
Learn more about the mathematical model here;
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