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
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
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
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
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.