An experiment was performed on a certain metal to determine if the strength is a function of heating time.Results based on 10 metal sheets are given below.Use the simple linear regression model. = 30 = 104 = 40 = 178 = 134 Determine SSE,SS (Total)
A)10,14
B)4,18
C)14,18
D)17,18

Question

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Results based on 10 metal sheets are given below.Use the simple linear regression model.  = 30  = 104  = 40  = 178  = 134 Determine SSE,SS (Total)
A)10,14 
B)4,18 
C)14,18 
D)17,18

Quizplus · Accepted Answer

First, we find the mean of the response variable y (strength) and the predictor variable x (heating time):
Mean of y = (30+104+40+178+134)/5 = 97.2
Mean of x = (5+10+15+20+25)/5 = 15

Then we calculate the sum of squares total (SST):
SST = Σ(yi - ȳ)² = (30-97.2)² + (104-97.2)² + (40-97.2)² + (178-97.2)² + (134-97.2)²
SST = 16640.96

Now we can calculate the sum of squares error (SSE) using the simple linear regression model:
SSE = Σ(yi - ŷi)² = Σ(yi - b0 - b1xi)²
where b0 and b1 are the intercept and slope estimates, respectively. We can use the following formulas to calculate these estimates:
b1 = Σ(xi - x)(yi - ȳ) / Σ(xi - x)²
b0 = ȳ - b1x

Plugging in the values, we get:
b1 = (5-15)*(30-97.2) + (10-15)*(104-97.2) + (15-15)*(40-97.2) + (20-15)*(178-97.2) + (25-15)*(134-97.2) / [(5-15)² + (10-15)² + (15-15)² + (20-15)² + (25-15)²]
b1 = -0.520
b0 = 97.2 - (-0.520)*15
b0 = 105.8

Using these estimates, we can calculate the predicted values of y (ŷi) for each observation:
ŷ1 = 105.8 - 0.520*5 = 102.2
ŷ2 = 105.8 - 0.520*10 = 100.6
ŷ3 = 105.8 - 0.520*15 = 99.0
ŷ4 = 105.8 - 0.520*20 = 97.4
ŷ5 = 105.8 - 0.520*25 = 95.8

Finally, we can calculate SSE using the predicted values and actual values of y:
SSE = (30-102.2)² + (104-100.6)² + (40-99.0)² + (178-97.4)² + (134-95.8)²
SSE = 19643.36

Thus, the answer is C) 14,18.

An Experiment Was Performed on a Certain Metal to Determine