Solution:
Representing the points on scatter plot
We will first find the line of best fit using the method of least square.
Line of best fit is the line inside the scatter plot which shows about equal number of points above or below the line.
Mean of X values =A=[tex]\frac{68+77+83+85+89+94+96+99}{6}=\frac{697}{8}=87.125[/tex]
Mean of Y values = B=[tex]\frac{403 +447 +457 +465 +489 +503 +543 +576}{8}=\frac{3883}{8}=485.375[/tex]
X values - Mean=X-A= -19.125, -10.125, -4.125, -2.125, 1.875, 6.875, 8.875, 11.875
Y Values - Mean = Y - B= -82.375,-38.375, -28.375,-20.375, 3.625,17.625,57.875,90.875
Slope= m=[tex]\frac{Sum(X-A)(Y-B)}{Sum(X-A)^2}=\frac{3839.868}{760.3748}=5.0499[/tex]
Y intercept
C=B- m A
=485.375 - (5.0499)×(87.125)
= 485.375- 439.9784
= 45.3966
The equation of best fit of line is , Y = m X + C i.e
y=5.05 x + 45.40 (Taking approx value of m and c)
When temperature is 106 degrees, then
Number of cones= 5.05×106 + 45.40
= 535.30 +45.40
= 580.70
=581(Round figure)
