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polet [3.4K]
2 years ago
14

In a teacher's math course, a linear regression line was calculated to predict

Mathematics
1 answer:
Marat540 [252]2 years ago
6 0

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; \hat y = 25.5 + 0.82·\mathbf{\hat x}

Where;

\hat y = Final exam score;

\hat x = The midterm score;

AJ score in the first test, \hat x = 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, \hat y = 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:

brainly.com/question/9339658

brainly.com/question/7361586

brainly.com/question/14747095

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A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour.
baherus [9]

A function that gives the amount that the plant earns per man-hour t years after it opens is \mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}

<h3><u>Solution:</u></h3>

Given that  

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.  

Amount earned by plant when it is opened = $80 per man-hour

As it is given that each year, the plants earns an additional of 5% per man hour

So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)

Amount earned by plant after two years is given as:

=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052

Similarly Amount earned by plant after three years =80 \times 1.05^{t}

\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is \mathrm{A}(t)=80 \times 1.05^{t}

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3 years ago
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