A company is interested in monitoring the thermal activity on an electronic device. They were advised to install five thermal sensors on the device.

Circle: Sensor

Big rectangle: Electronic device

Below are some temperature readings from the sensors in Fahrenheit:

Time (minutes)	Sensor 1	Sensor 2	Sensor 3	Sensor 4	Sensor 5
0	77oF	76oF	76oF	76oF	76oF
13	104oF	80oF	85oF	95oF	95oF
28	119oF	85oF	93oF	102oF	102oF
42	140oF	94oF	104oF	125oF	125oF
60	167oF	105oF	141oF	153oF	153oF

The company is interested to predict the temperature evolution at any location on the electronic device and not only at the locations of the sensors. With no further information about the sources of the heat, the engineers at the company are puzzled and completely rely on you to develop a model that captures the evolution of the temperature at any location on the electronic device.

(a)Construct a design matrix and a true response vector for your OLS regression model that predicts the evolution of temperature across both time and space of the electronic device. Clearly identify the predictors (factors) and the response. Explain the choice of your model.

(b)Complete the following table

R Squared
Adjusted R Squared
AIC
Standard Error
Number of Observations

(c)Run the model, report the values of the expected coefficients, and identify the significant factors of your temperature model. Clearly show your work.

(d)Identify if there are any outliers.

(e)Verify if the normality assumption is valid.

(f)Construct at least two relevant preliminary/supporting plots to identify the relevance of the chosen predictors in predicting the temperature.