Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Temp. 174 176 177 178 178 179 180 181
Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74
Temp. 184 184 184 184 184 185 185 186
Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94
Temp. 186 186 186 188 188 189 190 192
Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16
A)
Using the online linear regression calculator, the lie of best fit which models the data above is :
ŷ = 0.09386X - 15.55523
Where ;
X = independent variable
ŷ = predicted or dependent variable
- 15.55523 = intercept
0.09386 = gradient / slope
B)
Point estimate when tank temperature is 186
ŷ = 0.09386(186) - 15.55523
ŷ = 17.45796 - 15.55523
ŷ = 1.90273
C)
Residual error (y - ŷ), ŷ = 1.90273 when x = 186
(0.94 - 1.90273) = −0.96273
(1.85 - 1.90273) = −0.05273
(2.02 - 1.90273) = 0.11727
(2.64 - 1.90273) = 0.73727
D)
To determine the proportion of observed variation in efficiency ratio, we find the Coefficient of determination R^2, which can be found using the online Coefficient of determination calculator : the r^2 value obtained is 0.4433.
