Use the data in the table below to answer the attached questions.
x
-3
-2
-1
0
1
2
y
-6.7
-6.514
-6.247
-5.98
-5.713
-5.446
Which type of regression equation matches the data set in the table?
Which type of regression equation matches the data set in the table?
Linear
Quadratic
Exponential
5 answers
Linear
Question at position 3
3
1 point
Question at position 3
What is the regression equation that represents the data in the table?
What is the regression equation that represents the data in the table?
y=0.0072(0.2627)x
y=-5.9273x+0.2554
y=0.0072x2+0.2627x-5.9916
y=0.2554x-5.9723
3
1 point
Question at position 3
What is the regression equation that represents the data in the table?
What is the regression equation that represents the data in the table?
y=0.0072(0.2627)x
y=-5.9273x+0.2554
y=0.0072x2+0.2627x-5.9916
y=0.2554x-5.9723
To determine the regression equation that represents the data in the table, the linear regression equation y = mx + b can be used, where m is the slope and b is the y-intercept.
Using the data given:
x: -3, -2, -1, 0, 1, 2
y: -6.7, -6.514, -6.247, -5.98, -5.713, -5.446
Calculating the slope:
m = (Σxy - (Σx)(Σy)/n) / (Σx^2 - (Σx)^2/n)
m = ((-3*-6.7)+(-2*-6.514)+(-1*-6.247)+(0*-5.98)+(1*-5.713)+(2*-5.446) - (-15.946))/((9+4+1+0+1+4)-(36)/6)
m = (-20.1 + 13.0282)/14-(6)=(-7.0718)/8 = - 0,88
Calculating the y-intercept:
b = (Σy - mΣx) / n
b = (-6.7)-(-0,88*1)=
b = -5,812
Therefore, the regression equation that represents the data in the table is:
y = -0.88x - 5.812
Using the data given:
x: -3, -2, -1, 0, 1, 2
y: -6.7, -6.514, -6.247, -5.98, -5.713, -5.446
Calculating the slope:
m = (Σxy - (Σx)(Σy)/n) / (Σx^2 - (Σx)^2/n)
m = ((-3*-6.7)+(-2*-6.514)+(-1*-6.247)+(0*-5.98)+(1*-5.713)+(2*-5.446) - (-15.946))/((9+4+1+0+1+4)-(36)/6)
m = (-20.1 + 13.0282)/14-(6)=(-7.0718)/8 = - 0,88
Calculating the y-intercept:
b = (Σy - mΣx) / n
b = (-6.7)-(-0,88*1)=
b = -5,812
Therefore, the regression equation that represents the data in the table is:
y = -0.88x - 5.812
What is the value of the function for the data set when x=7?
What is the value of the function for the data set when x=7?
-4.1845
-4.2357
-3.8512
-3.7999
What is the value of the function for the data set when x=7?
-4.1845
-4.2357
-3.8512
-3.7999
To find the value of the function for the data set when x = 7, substitute x = 7 into the regression equation we previously found (y = -0.88x - 5.812):
y = -0.88(7) - 5.812
y = -6.16 - 5.812
y = -11.972
Therefore, when x = 7, the value of the function for the data set is approximately -11.972.
So, none of the given options-4.1845, -4.2357, -3.8512, -3.7999 match the calculated value.
y = -0.88(7) - 5.812
y = -6.16 - 5.812
y = -11.972
Therefore, when x = 7, the value of the function for the data set is approximately -11.972.
So, none of the given options-4.1845, -4.2357, -3.8512, -3.7999 match the calculated value.