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ruslelena [56]
3 years ago
10

Consider the following data points.

Mathematics
2 answers:
Hoochie [10]3 years ago
8 0

Answer:

the equation of the least-squares line for the data is: \hat Y=9.3+1.3x

Step-by-step explanation:

In a simple linear regression model, such as, \hat Y=b_0+b_1x, the coefficients bo and b1 are estimated through the method of least squares by the use of the equations:

b_1=\frac{S{xy}}{S_x^2}\\\\b_0=\bar{y}+b_1 \bar{x}

For the data provided you have to:

S_{xy}=\frac{\sum {(x_i-\bar x)(y_i-\bar y)}}{n-1}=3.25\\\\S_x^2=\frac{\sum {(x_i-\bar x)^2}}{n-1}=2.5\\\\\bar y=5.4, thus:

b_1=\frac{3.25}{2,5}=1.3\\\\b_0=5.4+1.3(3.0)=9.3

the equation of the least-squares line for the data is:

Y=9.3+1.3x

Naddika [18.5K]3 years ago
3 0

Answer:

y= 9.3 1.3

Step-by-step explanation:

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Which of the following equations describes the line shown below? Check all<br> that apply.
scoundrel [369]

Answer:

B. y = 2x - 2

E. y + 4 = 2(x + 1)

F. y - 6 = 2(x - 4)

Step-by-step explanation:

The equation of the line can be found using either the point-slope equation or the slope-intercept equation.

✔️Equation of the line in point-slope using the slope and the coordinates of the point (4, 6):

Slope = m = change in y/change in x

Using (4, 6) and (-1, -4),

m = (-4 - 6)/(-1 - 4)

m = -10/-5

m = 2

Substitute m = 2, and (a, b) = (4, 6) into the point-slope equation form y - b = m(x - a)

Thus:

y - 6 = 2(x - 4)

✔️Equation of the line in point-slope using the slope and the coordinates of the point (-1, -4):

Slope = m = 2

Substitute m = 2, and (a, b) = (-1, -4) into the point-slope equation form y - b = m(x - a)

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y - (-4) = 2(x - (-1))

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✔️Equation of the line in slope-intercept form, y = mx + b

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m = slope = 2

b = y-intercept = -2 (the point where the line intercepts the y-axis)

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y = 2x + (-2)

y = 2x - 2

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Answer:

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