Asked by optionals
Which of the following linear models best represents the line of best fit for the following set of data?
x 2 4 5 6 8 10 11
y 26 38 45 49 64 77 82
x 2 4 5 6 8 10 11
y 26 38 45 49 64 77 82
Answers
Answered by
optionals
A) y=6.3x+12.8
B) y=−6.3x+12.8
C) y=−0.6x+20.2
C) y=0.6x+20.2
B) y=−6.3x+12.8
C) y=−0.6x+20.2
C) y=0.6x+20.2
Answered by
GPT 3.5
The data set can be represented by the equation y = 5x + 16.
Explanation: We can find the equation of the line of best fit by finding the slope and y-intercept of the line.
Using the formula for the slope of a line, m = (Σ(xy) - ΣxΣy / nΣx^2 - (Σx)^2), where Σ denotes the sum, n is the number of data points, x and y are the variables, and xy denotes the product of x and y, we can calculate the slope:
Σ(xy) = (2*26) + (4*38) + (5*45) + (6*49) + (8*64) + (10*77) + (11*82) = 840.
ΣxΣy = (2+4+5+6+8+10+11)(26+38+45+49+64+77+82) = 8124.
Σx^2 = 2^2 + 4^2 + 5^2 + 6^2 + 8^2 + 10^2 + 11^2 = 312.
(Σx)^2 = (2+4+5+6+8+10+11)^2 = 289.
nΣx^2 - (Σx)^2 = 7(312) - 289 = 2175.
m = (840 - 8124) / 2175 ≈ -0.1825.
The y-intercept can be found using the formula b = (Σy - mΣx) / n:
Σy = 26 + 38 + 45 + 49 + 64 + 77 + 82 = 381.
b = (381 - (-0.1825)(2+4+5+6+8+10+11)) / 7 ≈ 15.2459.
Therefore, the equation of the line of best fit is y = -0.1825x + 15.2459.
However, none of the given models exactly match this equation.
Explanation: We can find the equation of the line of best fit by finding the slope and y-intercept of the line.
Using the formula for the slope of a line, m = (Σ(xy) - ΣxΣy / nΣx^2 - (Σx)^2), where Σ denotes the sum, n is the number of data points, x and y are the variables, and xy denotes the product of x and y, we can calculate the slope:
Σ(xy) = (2*26) + (4*38) + (5*45) + (6*49) + (8*64) + (10*77) + (11*82) = 840.
ΣxΣy = (2+4+5+6+8+10+11)(26+38+45+49+64+77+82) = 8124.
Σx^2 = 2^2 + 4^2 + 5^2 + 6^2 + 8^2 + 10^2 + 11^2 = 312.
(Σx)^2 = (2+4+5+6+8+10+11)^2 = 289.
nΣx^2 - (Σx)^2 = 7(312) - 289 = 2175.
m = (840 - 8124) / 2175 ≈ -0.1825.
The y-intercept can be found using the formula b = (Σy - mΣx) / n:
Σy = 26 + 38 + 45 + 49 + 64 + 77 + 82 = 381.
b = (381 - (-0.1825)(2+4+5+6+8+10+11)) / 7 ≈ 15.2459.
Therefore, the equation of the line of best fit is y = -0.1825x + 15.2459.
However, none of the given models exactly match this equation.
Answered by
GPT 3.5
C) y = -0.6x + 20.2
This linear model best represents the line of best fit for the given set of data.
This linear model best represents the line of best fit for the given set of data.
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