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wolverine [178]
3 years ago
7

Suppose the linear regression line y=2.1x+130 predicts sales based on the money spent on advertising. If x represents the dollar

s spent in advertising, and yea represents the company sales in dollars, about how much can the company expects in sales if it spends $150 in advertising
Mathematics
1 answer:
slega [8]3 years ago
5 0

Linear regression line y=2.1x+130 predicts sales based on the money spent on advertising.

Linear regression represents the relationship between two variables. the value of y depends on the value of x.

x represents the dollars spent in advertising and y represents the company sales in dollars.

We need to find out sales y when $150 spends on advertising.

Plug in 150 for x and find out y

y = 2.1 x + 130

y = 2.1 (150) + 130

y= 445

The company expects $445 in sales

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Let the equations be:

a_1x+b_1y+c_1=0 and

a_2x+b_2y+c_2=0

1. There exists exactly one solution:

\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}

2. There exists infinitely many solutions i.e. lines are identical.

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}

3. There exists No solutions i.e. lines are parallel and will never intersect.

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}

Now, let us have a look at the given pair of lines:

Option a)

2 x + 8 y = 15\\4 x + 16 y = 30.

The ratio:

\dfrac{2}{4}=\dfrac{8}{16}=\dfrac{15}{30} = \dfrac{1}{2}

Hence, the lines are identical, infinite solutions.

Option b)

2 x - y = 18\\4 x + 2 y = 38

The ratio:

\dfrac{2}{4}\neq \dfrac{-1}{2}

Hence, exactly one solution.

Option c)

4 x + 7 y = 17\\8 x -14 y = 36

The ratio:

\dfrac{4}{8}\neq \dfrac{-7}{14}\\\dfrac{1}{2}\neq \dfrac{-1}{2}

Hence, exactly one solution.

Option d)

4 x - 3 y = 16\\8 x - 6 y = 34.

The ratio:

\dfrac{4}{8}= \dfrac{-3}{-6}\neq\dfrac{16}{34}\\\Rightarrow \dfrac{1}{2}= \dfrac{1}{2}\neq\dfrac{8}{17}

Hence, There is no solution.

The correct answer is:

4 x -3 y = 16 and

8 x -6 y = 34 are the equations that have no solution.

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