Identify lines of best fit - HiSET

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Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 & 3.5 \ 2 & 4.7\ 3 & 6.0\ 4 & 7.8 \end{matrix}$

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The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$= $\frac{248.4-220}{120-100}$$

$= $\frac{28.4}{20}$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{22}{4}$ = 5.5$

The equation of the linear regression line is .

Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 &10.0 \ 2 &8.7\ 3 & 7.1 \ 4 & 5.0 \end{matrix}$

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The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$= $\frac{274.8 - 308}{120-100 }$$

$= $\frac{-33.2}{20 }$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{30.8}{4}$ = 7.7$

The linear regression line is the line of the equation .

Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 & 3.5 \ 2 & 4.7\ 3 & 6.0\ 4 & 7.8 \end{matrix}$

Tap to see back →

The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$= $\frac{248.4-220}{120-100}$$

$= $\frac{28.4}{20}$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{22}{4}$ = 5.5$

The equation of the linear regression line is .

Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 &10.0 \ 2 &8.7\ 3 & 7.1 \ 4 & 5.0 \end{matrix}$

Tap to see back →

The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$= $\frac{274.8 - 308}{120-100 }$$

$= $\frac{-33.2}{20 }$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{30.8}{4}$ = 7.7$

The linear regression line is the line of the equation .

Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 & 3.5 \ 2 & 4.7\ 3 & 6.0\ 4 & 7.8 \end{matrix}$

Tap to see back →

The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$= $\frac{248.4-220}{120-100}$$

$= $\frac{28.4}{20}$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{22}{4}$ = 5.5$

The equation of the linear regression line is .

Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 &10.0 \ 2 &8.7\ 3 & 7.1 \ 4 & 5.0 \end{matrix}$

Tap to see back →

The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$= $\frac{274.8 - 308}{120-100 }$$

$= $\frac{-33.2}{20 }$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{30.8}{4}$ = 7.7$

The linear regression line is the line of the equation .

Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 & 3.5 \ 2 & 4.7\ 3 & 6.0\ 4 & 7.8 \end{matrix}$

Tap to see back →

The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y = 3.5 + 4.7 + 6.0 + 7.8 = 22.0$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(3.5 )+ 2(4.7)+ 3(6.0)+ 4 (7.8) = 3.5 + 9.4 + 18.0 + 31.2 = 62.1$

Substituting:

$= $\frac{248.4-220}{120-100}$$

$= $\frac{28.4}{20}$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{22}{4}$ = 5.5$

The equation of the linear regression line is .

Determine the linear regression line for the following paired data:

$\begin{matrix} $\underline{x }$&$\underline{y}$ \ 1 &10.0 \ 2 &8.7\ 3 & 7.1 \ 4 & 5.0 \end{matrix}$

Tap to see back →

The formula for a regression line for a set of paired data is the line of the equation

$y $=b_{1}$x+ $b_{0}$$ ,

where

and

.

, the number of pairs.

$\sum x$ is the sum of the values:

$\sum x = 1 + 2 + 3 + 4 = 10$

$\sum y$ is the sum of the values:

$\sum y= 10.0+8.7+ 7.1 +5.0 = 30.8$

$\sum $x^{2}$$ is the sum of the squares of the values:

$\sum $x^{2}$ = $1^{2}$ + $2^{2}$ + 3 ^{2} + 4 ^{2} = 1 + 4 + 9 + 16 = 30$

$\sum xy$ is the sum of the products:

$\sum xy = 1(10.0 )+ 2(8.7)+ 3(7.1)+ 4 (5.0) = 10.0+ 17.4+21.3 + 20.0= 68.7$

Substituting:

$= $\frac{274.8 - 308}{120-100 }$$

$= $\frac{-33.2}{20 }$$

$\overline{x}$ and $\overline{y}$ are the arithmetic means of the and values, respectively - the sums divided by the number of values:

$$\overline{x}$ = $\frac{\sum x}{n}$ = $\frac{10}{4}$ = 2.5$

$$\overline{y}$ = $\frac{\sum y}{n}$ = $\frac{30.8}{4}$ = 7.7$

The linear regression line is the line of the equation .