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Blizzard [7]
3 years ago
14

The equation for the line of best fit for a data set is y = 2x + 1.5. If the point (1, 4) is in the data set, what is the residu

al of 1? 0.5 3.5 4.0 7.5
Mathematics
2 answers:
andriy [413]3 years ago
3 0
It is related to econometrics, however using simple algebraic logic we can solve this problem. General formula with residual is y=2x+1.5+r, where r is a residual. Plugging the pair into the formula, we obtain that 4=2*1+1.5+r and r=0.5
Zina [86]3 years ago
3 0

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

y=2x+1.5

If the point (1,4) is in the data set.

we need to find the residual of 1.

At x = 1,

y=2x+1.5\\\\y=2\times 1+1.5\\\\y=2+1.5\\\\y=3.5

So, At x = 1, the value of y = 3.5

As we know that

Residual\ value=Estimate\ value-Actual\ value\\\\Residual\ value=4-3.5\\\\Residual\ value=0.5

Hence, The residual of 1 is 0.5.

Thus, First option is correct.

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A professor went to a website for rating professors and looked up the quality rating and also the "easiness" of the six full-tim
Marat540 [252]

We are asked to determine the correlation factor "r" of the given table. To do that we will first label the column for "Quality" as "x" and the column for "Easiness" as "y". Like this:

Now, we create another column with the product of "x" and "y". Like this:

Now, we will add another column with the squares of the values of "x". Like this:

Now, we add another column with the squares of the values of "y":

Now, we sum the values on each of the columns:

Now, to get the correlation factor we use the following formula:

r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)}}

Where:

\begin{gathered} \Sigma xy=\text{ sum of the column of xy} \\ \Sigma x=\text{ sum of the column x} \\ \Sigma y=\text{ sum of the column y} \\ \Sigma x^2=\text{ sum of the column x\textasciicircum2} \\ \Sigma y^2=\text{ sum of the column y\textasciicircum2} \\ n=\text{ number of rows} \end{gathered}

Now we substitute the values, we get:

r=\frac{\left(6)(70.56)-(25.2)(16.4\right)}{\sqrt{((6)(107.12)-(25.2)^2)((6)(47.82)-(16.4)^2)}}

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r=0.858

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7 0
1 year ago
PLEASE HELP SOMEONE!!!
evablogger [386]

Answer:

y = -2x

Step-by-step explanation:

For direct variation:  y = kx, where k is the constant of proportionality.

Given that Y equals -12 when x equals 6, we have -12 = k(6).  Solve this for k by dividing both sides by 6:

k = -12/6 => k = -2

Then the "direct variation equation" here is y = -2x.

3 0
3 years ago
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Gre4nikov [31]

Answer:

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Step-by-step explanation:

180 degree rotation = (x,y)---(-x, -y)

hence, if k=(3,2)

then k' = (-3, -2)

90 degree rotation clockwise= (x,y)--(y,-x)

hence if, A=(-5 , -2)

then, A'= (-2, 5)

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3 years ago
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givi [52]

Answer:

Step-by-step explanation:

A

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3 years ago
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