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Ghella [55]
3 years ago
6

Question 5(Multiple Choice Worth 4 points) Which number is the largest? 1.2 × 104, 4.5 × 10−3, 3.8 × 103, 7.5 × 103 1.2 × 104 4.

5 × 10−3 3.8 × 103 7.5 × 103
Mathematics
1 answer:
Andrew [12]3 years ago
8 0

Answer:

  • 1.2 × 10^4

Step-by-step explanation:

<u>Which number is the largest? </u>

  • 1.2 × 10^4
  • 4.5 × 10^-3
  • 3.8 × 10^3
  • 7.5 × 10^3

The first one is the largest as it has the greatest power

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Answer:

The equation of the regression line is:

y~=~234.56158 ~-~ 2.95835 \cdot x

Step-by-step explanation:

The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance.

We have the following data:

\begin{array}{c|ccccccccc}X&50&55&50&79&44&37&70&45&49\\Y&152&48&22&35&43&171&13&185&25\end{array}

To find the line of best fit for the points:

Step 1: Find X\cdot X and X\cdot Y as it was done in the table

Step 2: Find the sum of every column:

\sum{X} = 479 ~,~ \sum{Y} = 694 ~,~ \sum{X \cdot Y} = 32784 ~,~ \sum{X^2} = 26897

Step 3: Use the following equations to find a and b:

\begin{aligned}        a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} =             \frac{ 694 \cdot 26897 - 479 \cdot 32784}{ 9 \cdot 26897 - 479^2} \approx 234.56158 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 9 \cdot 32784 - 479 \cdot 694 }{ 9 \cdot 26897 - \left( 479 \right)^2} \approx -2.95835\end{aligned}

Step 4: Assemble the equation of a line

\begin{aligned} y~&=~a ~+~ b \cdot x \\y~=~234.56158 ~-~ 2.95835\cdot x\end{aligned}

The graph of the regression line is:

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