# You are trying to determine the temperature at which to conduct a m...

## Question

You are trying to determine the temperature at which to conduct a manufacturing process that generates the maximum yield. You have measured the yield at different temperatures.

Dataset: Yield_and_temperature.csv

The quadratic model equation for the population will be: yi = β0 + β1 x1i + β2 x2i + εi where x1 is temperature and x2 is temperature squared.

Fill in the values for the ANOVA table.

## Solution Preview

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# create new variable which is the square of temperature squared
data\$temperature2 <- data\$temperature*data\$temperature
# fitting regression model
model <- lm (yield~temperature+temperature2, data= data)
# obtaining anova and other statistic tables
summary (model)
aov (model)
#95% confidence interval
confint (model)
R Output is given below:
Call:
lm(formula = yield ~ temperature + temperature2, data = data)
Residuals:
Min       1Q   Median       3Q      Max
-3.00699 -1.41958 0.03497 1.32867 2.10490
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -7.121e+02 5.437e+01 -13.10 1.10e-06 ***
temperature   2.391e+00 1.512e-01   15.81 2.56e-07 ***
temperature2 -1.650e-03 1.042e-04 -15.84 2.52e-07 ***...

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