High School

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A data set is given below.

(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between \( x \) and \( y \).

(b) Given that \(\bar{x}=3.8333\), \(s_x=2.0412\), \(\bar{y}=4.0167\), \(s_y=1.3393\), and \(r=-0.8986\), determine the least-squares regression line.

(c) Graph the least-squares regression line on the scatter diagram drawn in part (a).

(a) Choose the correct graph below.

A.
B.
C.

There appears to be ___________ relationship.

(b) \(\hat{y} = x + \) (Round to three decimal places as needed.)

Answer :

The equation y = x + (the value you calculated for b) on the same graph where you plotted the scatter diagram.

The correct scatter diagram and the least-squares regression line for the given data set is shown below.

(a) The scatter diagram is shown below,

There is a strong negative relationship appears to exist between x and y.

(b) The least-squares regression line is given by,

[tex]$$y = a + bx$$[/tex]

where, a is the y-intercept and b is the slope.

We know that,

a = y - (b * x)

where y is the mean of y and x is the mean of x.

Given the values you provided:

x = 3.8333

sx​ = 2.0412

y = 4.0167

sy​ = 1.3393

r = -0.8986

[tex]$$b = \frac{r_{xy}sy}{sx}$$$$a = \bar{y} - b \bar{x}$$[/tex]

where, rxy is the correlation coefficient, sx and sy are the standard deviation of x and y respectively,

[tex]$\bar{x}$ and $\bar{y}$[/tex] are the mean of x and y respectively.

Therefore, we have, b = -2.758 and a = 12.033y

= 12.033 - 2.758x

For more related questions on scatter diagram:

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