a) We can see from the table that with the increase in value of x , there is decrease in value of y , hence we can say that coefficient of correlation is negative b) Equation of least squares is y = − 2.9866 x + 24.92 and correlation coefficient r = − 0.9995 Plot is c) Predicted value of y at x = 2.4 is 17.752 Given information: Five points x −4 −3 −1 3 5 y 3.7 33.7 27.5 16.4 9.8 Formula used: Slope, m = ∑ i = 1 n ( x i − X ¯ ) ( y i − Y ¯ ) ∑ i = 1 n ( x i − X ¯ ) 2 Y axis intercept, b = Y ¯ − m X ¯ Correlation Coefficient, r = ∑ i = 1 n ( x i − X ¯ ) ( y i − Y ¯ ) ∑ i = 1 n ( x i − X ¯ ) 2 ∑ i = 1 n ( y i − Y ¯ ) 2 Where x i and y i are the i th entry of x and y ; X ¯ and Y ¯ are means of x and y Calculation: Step 1: Calculate the mean of x and y X ¯ = ( − 4 ) + ( − 3 ) + ( − 1 ) + 3 + 5 5 = 0 Y ¯ = 37.2 + 33.7 + 27.5 + 16.4 + 9.8 5 = 24.92 Step 2: Plot the table as shown i x i y i x i − X ¯ y i − Y ¯ ( x i − X ¯ ) 2 ( x i − X ¯ ) ( y i − Y ¯ ) ( y i − Y ¯ ) 2 1 -4 37.2 -4 12.28 16 -49.12 150.7984 2 -3 33.7 -3 8.78 9 -26.34 77.0884 3 -1 27.5 -1 2.58 1 -2.58 6.6564 4 3 16.4 3 -8.52 9 -25.56 72.5904 5 5 9.8 5 -15.12 25 -75.6 228.6144 ∑ i = 1 n ( x i − X ¯ ) 2 = 60 ∑ i = 1 n ( x i − X ¯ ) ( y i − Y ¯ ) = − 179.2 ∑ i = 1 n ( y i − Y ¯ ) 2 = 535.7480 Step 3: Calculate the slope m = ∑ i = 1 n ( x i − X ¯ ) ( y i − Y ¯ ) ∑ i = 1 n ( x i − X ¯ ) 2 = − 179.2 60 ≈ − 2.9866 Step 4: Calculate y intercept b = Y ¯ − m X ¯ = 24.92 − ( − 2.9866 × 0 ) ≈ 24.92 The slope of the line is − 2.9866 and y intercept is 24.92 Using slope intercept form, y = m x + b ,equation is y = − 2.9866 x + 24.92 ; Step 5: Draw the scatter plot Step 6: Calculate the Correlation coefficient r = ∑ i = 1 n ( x i − X ¯ ) ( y i − Y ¯ ) ∑ i = 1 n ( x i − X ¯ ) 2 ∑ i = 1 n ( y i − Y ¯ ) 2 = − 179.2 60 × 535.7480 ≈ − 0.9995 Step 7: Prediction for x = 2.4 ; plug x = 2.4 in y = − 2.9866 x + 24.92 y = − 2.9866 ( 2.4 ) + 24.92 = 17.752

Question

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Answer 1

Question

Chapter 2.1, Problem 104E

To determine

To determine:

a) We can see from the table that with the increase in value of $x$ , there is decrease in value of $y$ , hence we can say that coefficient of correlation is negative

b) Equation of least squares is $y=−2.9866x+24.92$ and correlation coefficient $r=−0.9995$

Plot is

c) Predicted value of y at $x=2.4$ is $17.752$

Given information: Five points

$x$ −4 −3 −1 3 5

$y$ 3.7 33.7 27.5 16.4 9.8

Formula used: Slope, $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2$

Y axis intercept, $b= Y ¯ −m X ¯$

Correlation Coefficient, $r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2$

Where $x i$ and $y i$ are the $i$ th entry of $x$ and $y$ ; $X ¯$ and $Y ¯$ are means of $x$ and $y$

Calculation:

Step 1: Calculate the mean of $x$ and $y$
$X ¯ = (−4)+(−3)+(−1)+3+5 5 =0 Y ¯ = 37.2+33.7+27.5+16.4+9.8 5 =24.92$
Step 2: Plot the table as shown

$i$ $x i$ $y i$ $x i − X ¯$ $y i − Y ¯$ $( x i − X ¯ ) 2$ $( x i − X ¯ )( y i − Y ¯ )$ $( y i − Y ¯ ) 2$

1 -4 37.2 -4 12.28 16 -49.12 150.7984

2 -3 33.7 -3 8.78 9 -26.34 77.0884

3 -1 27.5 -1 2.58 1 -2.58 6.6564

4 3 16.4 3 -8.52 9 -25.56 72.5904

5 5 9.8 5 -15.12 25 -75.6 228.6144

$∑ i=1 n ( x i − X ¯ ) 2 =60$ $∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$ $∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$

Step 3: Calculate the slope $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 = −179.2 60 ≈−2.9866$

Step 4: Calculate $y$ intercept $b= Y ¯ −m X ¯ =24.92−(−2.9866×0)≈24.92$

The slope of the line is $−2.9866$ and y intercept is $24.92$

Using slope intercept form, $y=mx+b$ ,equation is $y=−2.9866x+24.92$ ;

Step 5: Draw the scatter plot

Step 6: Calculate the Correlation coefficient
$r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2 = −179.2 60 × 535.7480 ≈−0.9995$
Step 7: Prediction for $x=2.4$ ; plug $x=2.4$ in $y=−2.9866x+24.92$
$y=−2.9866(2.4)+24.92=17.752$

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Answer 2

Question

Chapter 2.1, Problem 104E

To determine

To determine:

a) We can see from the table that with the increase in value of $x$ , there is decrease in value of $y$ , hence we can say that coefficient of correlation is negative

b) Equation of least squares is $y=−2.9866x+24.92$ and correlation coefficient $r=−0.9995$

Plot is

c) Predicted value of y at $x=2.4$ is $17.752$

Given information: Five points

$x$ −4 −3 −1 3 5

$y$ 3.7 33.7 27.5 16.4 9.8

Formula used: Slope, $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2$

Y axis intercept, $b= Y ¯ −m X ¯$

Correlation Coefficient, $r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2$

Where $x i$ and $y i$ are the $i$ th entry of $x$ and $y$ ; $X ¯$ and $Y ¯$ are means of $x$ and $y$

Calculation:

Step 1: Calculate the mean of $x$ and $y$
$X ¯ = (−4)+(−3)+(−1)+3+5 5 =0 Y ¯ = 37.2+33.7+27.5+16.4+9.8 5 =24.92$
Step 2: Plot the table as shown

$i$ $x i$ $y i$ $x i − X ¯$ $y i − Y ¯$ $( x i − X ¯ ) 2$ $( x i − X ¯ )( y i − Y ¯ )$ $( y i − Y ¯ ) 2$

1 -4 37.2 -4 12.28 16 -49.12 150.7984

2 -3 33.7 -3 8.78 9 -26.34 77.0884

3 -1 27.5 -1 2.58 1 -2.58 6.6564

4 3 16.4 3 -8.52 9 -25.56 72.5904

5 5 9.8 5 -15.12 25 -75.6 228.6144

$∑ i=1 n ( x i − X ¯ ) 2 =60$ $∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$ $∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$

Step 3: Calculate the slope $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 = −179.2 60 ≈−2.9866$

Step 4: Calculate $y$ intercept $b= Y ¯ −m X ¯ =24.92−(−2.9866×0)≈24.92$

The slope of the line is $−2.9866$ and y intercept is $24.92$

Using slope intercept form, $y=mx+b$ ,equation is $y=−2.9866x+24.92$ ;

Step 5: Draw the scatter plot

Step 6: Calculate the Correlation coefficient
$r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2 = −179.2 60 × 535.7480 ≈−0.9995$
Step 7: Prediction for $x=2.4$ ; plug $x=2.4$ in $y=−2.9866x+24.92$
$y=−2.9866(2.4)+24.92=17.752$

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2.1, Problem 104E

To determine

To determine:

a) We can see from the table that with the increase in value of $x$ , there is decrease in value of $y$ , hence we can say that coefficient of correlation is negative

b) Equation of least squares is $y=−2.9866x+24.92$ and correlation coefficient $r=−0.9995$

Plot is

c) Predicted value of y at $x=2.4$ is $17.752$

Given information: Five points

$x$ −4 −3 −1 3 5

$y$ 3.7 33.7 27.5 16.4 9.8

Formula used: Slope, $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2$

Y axis intercept, $b= Y ¯ −m X ¯$

Correlation Coefficient, $r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2$

Where $x i$ and $y i$ are the $i$ th entry of $x$ and $y$ ; $X ¯$ and $Y ¯$ are means of $x$ and $y$

Calculation:

Step 1: Calculate the mean of $x$ and $y$
$X ¯ = (−4)+(−3)+(−1)+3+5 5 =0 Y ¯ = 37.2+33.7+27.5+16.4+9.8 5 =24.92$
Step 2: Plot the table as shown

$i$ $x i$ $y i$ $x i − X ¯$ $y i − Y ¯$ $( x i − X ¯ ) 2$ $( x i − X ¯ )( y i − Y ¯ )$ $( y i − Y ¯ ) 2$

1 -4 37.2 -4 12.28 16 -49.12 150.7984

2 -3 33.7 -3 8.78 9 -26.34 77.0884

3 -1 27.5 -1 2.58 1 -2.58 6.6564

4 3 16.4 3 -8.52 9 -25.56 72.5904

5 5 9.8 5 -15.12 25 -75.6 228.6144

$∑ i=1 n ( x i − X ¯ ) 2 =60$ $∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$ $∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$

Step 3: Calculate the slope $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 = −179.2 60 ≈−2.9866$

Step 4: Calculate $y$ intercept $b= Y ¯ −m X ¯ =24.92−(−2.9866×0)≈24.92$

The slope of the line is $−2.9866$ and y intercept is $24.92$

Using slope intercept form, $y=mx+b$ ,equation is $y=−2.9866x+24.92$ ;

Step 5: Draw the scatter plot

Step 6: Calculate the Correlation coefficient
$r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2 = −179.2 60 × 535.7480 ≈−0.9995$
Step 7: Prediction for $x=2.4$ ; plug $x=2.4$ in $y=−2.9866x+24.92$
$y=−2.9866(2.4)+24.92=17.752$

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2.1, Problem 104E

To determine

To determine:

a) We can see from the table that with the increase in value of $x$ , there is decrease in value of $y$ , hence we can say that coefficient of correlation is negative

b) Equation of least squares is $y=−2.9866x+24.92$ and correlation coefficient $r=−0.9995$

Plot is

c) Predicted value of y at $x=2.4$ is $17.752$

Given information: Five points

$x$ −4 −3 −1 3 5

$y$ 3.7 33.7 27.5 16.4 9.8

Formula used: Slope, $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2$

Y axis intercept, $b= Y ¯ −m X ¯$

Correlation Coefficient, $r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2$

Where $x i$ and $y i$ are the $i$ th entry of $x$ and $y$ ; $X ¯$ and $Y ¯$ are means of $x$ and $y$

Calculation:

Step 1: Calculate the mean of $x$ and $y$
$X ¯ = (−4)+(−3)+(−1)+3+5 5 =0 Y ¯ = 37.2+33.7+27.5+16.4+9.8 5 =24.92$
Step 2: Plot the table as shown

$i$ $x i$ $y i$ $x i − X ¯$ $y i − Y ¯$ $( x i − X ¯ ) 2$ $( x i − X ¯ )( y i − Y ¯ )$ $( y i − Y ¯ ) 2$

1 -4 37.2 -4 12.28 16 -49.12 150.7984

2 -3 33.7 -3 8.78 9 -26.34 77.0884

3 -1 27.5 -1 2.58 1 -2.58 6.6564

4 3 16.4 3 -8.52 9 -25.56 72.5904

5 5 9.8 5 -15.12 25 -75.6 228.6144

$∑ i=1 n ( x i − X ¯ ) 2 =60$ $∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$ $∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$

Step 3: Calculate the slope $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 = −179.2 60 ≈−2.9866$

Step 4: Calculate $y$ intercept $b= Y ¯ −m X ¯ =24.92−(−2.9866×0)≈24.92$

The slope of the line is $−2.9866$ and y intercept is $24.92$

Using slope intercept form, $y=mx+b$ ,equation is $y=−2.9866x+24.92$ ;

Step 5: Draw the scatter plot

Step 6: Calculate the Correlation coefficient
$r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2 = −179.2 60 × 535.7480 ≈−0.9995$
Step 7: Prediction for $x=2.4$ ; plug $x=2.4$ in $y=−2.9866x+24.92$
$y=−2.9866(2.4)+24.92=17.752$

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 2.1, Problem 104E

To determine

To determine:

a) We can see from the table that with the increase in value of $x$ , there is decrease in value of $y$ , hence we can say that coefficient of correlation is negative

b) Equation of least squares is $y=−2.9866x+24.92$ and correlation coefficient $r=−0.9995$

Plot is

c) Predicted value of y at $x=2.4$ is $17.752$

Given information: Five points

$x$ −4 −3 −1 3 5

$y$ 3.7 33.7 27.5 16.4 9.8

Formula used: Slope, $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2$

Y axis intercept, $b= Y ¯ −m X ¯$

Correlation Coefficient, $r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2$

Where $x i$ and $y i$ are the $i$ th entry of $x$ and $y$ ; $X ¯$ and $Y ¯$ are means of $x$ and $y$

Calculation:

Step 1: Calculate the mean of $x$ and $y$
$X ¯ = (−4)+(−3)+(−1)+3+5 5 =0 Y ¯ = 37.2+33.7+27.5+16.4+9.8 5 =24.92$
Step 2: Plot the table as shown

$i$ $x i$ $y i$ $x i − X ¯$ $y i − Y ¯$ $( x i − X ¯ ) 2$ $( x i − X ¯ )( y i − Y ¯ )$ $( y i − Y ¯ ) 2$

1 -4 37.2 -4 12.28 16 -49.12 150.7984

2 -3 33.7 -3 8.78 9 -26.34 77.0884

3 -1 27.5 -1 2.58 1 -2.58 6.6564

4 3 16.4 3 -8.52 9 -25.56 72.5904

5 5 9.8 5 -15.12 25 -75.6 228.6144

$∑ i=1 n ( x i − X ¯ ) 2 =60$ $∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$ $∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$

Step 3: Calculate the slope $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 = −179.2 60 ≈−2.9866$

Step 4: Calculate $y$ intercept $b= Y ¯ −m X ¯ =24.92−(−2.9866×0)≈24.92$

The slope of the line is $−2.9866$ and y intercept is $24.92$

Using slope intercept form, $y=mx+b$ ,equation is $y=−2.9866x+24.92$ ;

Step 5: Draw the scatter plot

Step 6: Calculate the Correlation coefficient
$r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2 = −179.2 60 × 535.7480 ≈−0.9995$
Step 7: Prediction for $x=2.4$ ; plug $x=2.4$ in $y=−2.9866x+24.92$
$y=−2.9866(2.4)+24.92=17.752$

Answer 6

Chapter 2.1, Problem 104E

To determine

To determine:

a) We can see from the table that with the increase in value of $x$ , there is decrease in value of $y$ , hence we can say that coefficient of correlation is negative

b) Equation of least squares is $y=−2.9866x+24.92$ and correlation coefficient $r=−0.9995$

Plot is

c) Predicted value of y at $x=2.4$ is $17.752$

Given information: Five points

$x$ −4 −3 −1 3 5

$y$ 3.7 33.7 27.5 16.4 9.8

Formula used: Slope, $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2$

Y axis intercept, $b= Y ¯ −m X ¯$

Correlation Coefficient, $r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2$

Where $x i$ and $y i$ are the $i$ th entry of $x$ and $y$ ; $X ¯$ and $Y ¯$ are means of $x$ and $y$

Calculation:

Step 1: Calculate the mean of $x$ and $y$
$X ¯ = (−4)+(−3)+(−1)+3+5 5 =0 Y ¯ = 37.2+33.7+27.5+16.4+9.8 5 =24.92$
Step 2: Plot the table as shown

$i$ $x i$ $y i$ $x i − X ¯$ $y i − Y ¯$ $( x i − X ¯ ) 2$ $( x i − X ¯ )( y i − Y ¯ )$ $( y i − Y ¯ ) 2$

1 -4 37.2 -4 12.28 16 -49.12 150.7984

2 -3 33.7 -3 8.78 9 -26.34 77.0884

3 -1 27.5 -1 2.58 1 -2.58 6.6564

4 3 16.4 3 -8.52 9 -25.56 72.5904

5 5 9.8 5 -15.12 25 -75.6 228.6144

$∑ i=1 n ( x i − X ¯ ) 2 =60$ $∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$ $∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$

Step 3: Calculate the slope $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 = −179.2 60 ≈−2.9866$

Step 4: Calculate $y$ intercept $b= Y ¯ −m X ¯ =24.92−(−2.9866×0)≈24.92$

The slope of the line is $−2.9866$ and y intercept is $24.92$

Using slope intercept form, $y=mx+b$ ,equation is $y=−2.9866x+24.92$ ;

Step 5: Draw the scatter plot

Step 6: Calculate the Correlation coefficient
$r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2 = −179.2 60 × 535.7480 ≈−0.9995$
Step 7: Prediction for $x=2.4$ ; plug $x=2.4$ in $y=−2.9866x+24.92$
$y=−2.9866(2.4)+24.92=17.752$

Answer 7

Chapter 2.1, Problem 104E

To determine

To determine:

a) We can see from the table that with the increase in value of $x$ , there is decrease in value of $y$ , hence we can say that coefficient of correlation is negative

b) Equation of least squares is $y=−2.9866x+24.92$ and correlation coefficient $r=−0.9995$

Plot is

c) Predicted value of y at $x=2.4$ is $17.752$

Given information: Five points

$x$ −4 −3 −1 3 5

$y$ 3.7 33.7 27.5 16.4 9.8

Formula used: Slope, $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2$

Y axis intercept, $b= Y ¯ −m X ¯$

Correlation Coefficient, $r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2$

Where $x i$ and $y i$ are the $i$ th entry of $x$ and $y$ ; $X ¯$ and $Y ¯$ are means of $x$ and $y$

Calculation:

Step 1: Calculate the mean of $x$ and $y$
$X ¯ = (−4)+(−3)+(−1)+3+5 5 =0 Y ¯ = 37.2+33.7+27.5+16.4+9.8 5 =24.92$
Step 2: Plot the table as shown

$i$ $x i$ $y i$ $x i − X ¯$ $y i − Y ¯$ $( x i − X ¯ ) 2$ $( x i − X ¯ )( y i − Y ¯ )$ $( y i − Y ¯ ) 2$

1 -4 37.2 -4 12.28 16 -49.12 150.7984

2 -3 33.7 -3 8.78 9 -26.34 77.0884

3 -1 27.5 -1 2.58 1 -2.58 6.6564

4 3 16.4 3 -8.52 9 -25.56 72.5904

5 5 9.8 5 -15.12 25 -75.6 228.6144

$∑ i=1 n ( x i − X ¯ ) 2 =60$ $∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$ $∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$

Step 3: Calculate the slope $m= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 = −179.2 60 ≈−2.9866$

Step 4: Calculate $y$ intercept $b= Y ¯ −m X ¯ =24.92−(−2.9866×0)≈24.92$

The slope of the line is $−2.9866$ and y intercept is $24.92$

Using slope intercept form, $y=mx+b$ ,equation is $y=−2.9866x+24.92$ ;

Step 5: Draw the scatter plot

Step 6: Calculate the Correlation coefficient
$r= ∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) ∑ i=1 n ( x i − X ¯ ) 2 ∑ i=1 n ( y i − Y ¯ ) 2 = −179.2 60 × 535.7480 ≈−0.9995$
Step 7: Prediction for $x=2.4$ ; plug $x=2.4$ in $y=−2.9866x+24.92$
$y=−2.9866(2.4)+24.92=17.752$

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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See solution

Answer 11

Concept explainers

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Chapter 2 Solutions

$i$	$x i$	$y i$	$x i − X ¯$	$y i − Y ¯$	$( x i − X ¯ ) 2$	$( x i − X ¯ )( y i − Y ¯ )$	$( y i − Y ¯ ) 2$
1	-4	37.2	-4	12.28	16	-49.12	150.7984
2	-3	33.7	-3	8.78	9	-26.34	77.0884
3	-1	27.5	-1	2.58	1	-2.58	6.6564
4	3	16.4	3	-8.52	9	-25.56	72.5904
5	5	9.8	5	-15.12	25	-75.6	228.6144
					$∑ i=1 n ( x i − X ¯ ) 2 =60$	$∑ i=1 n ( x i − X ¯ )( y i − Y ¯ ) =−179.2$	$∑ i=1 n ( y i − Y ¯ ) 2 =535.7480$