(Solved): please do all 5, use python for part 5  There are 6 sample points as shown in following fi ...

please do all 5, use python for part 5 

There are 6 sample points as shown in following figure. \( X \) stands for independent variable, and \( Y \) stands for dependent variable. It is known that: \[ \mathrm{p} 1=\{12,21\} ; \mathrm{p} 2=\{20,40\} ; \mathrm{p} 3=\{25,9\} ; \mathrm{p} 4=\{36,18\} ; \mathrm{p} 5=\{40,60\} ; \mathrm{p} 6=\{50,61\} \] Assume that a linear regression model will be built to fit these data points. Question 1 (Fill-in-the-blank): Solve the optimized values of \( \boldsymbol{\theta}_{0} \) and \( \boldsymbol{\theta}_{1} \) of the linear regression model. Write the answer in following space: \[ \boldsymbol{\theta}_{0}=\ldots \text { (2 marks) } \] \( \boldsymbol{\theta}_{1}=\ldots \) (2 marks) What is the predicted value of \( \mathrm{p} 5 \) ? Write the answer in following space: (2 marks) Question 3 (Fill-in-the-blank): How much of the Mean Squared Error? Write the answer in following space: (2 marks) Question 4 (Fill-in-the-blank): If there is new data point whose independent value \( \mathrm{X} \) is 60 , please predict its dependent value. Write the answer in following space: (2 marks) Question 5 (4 marks): Submit your bug-free source code with name as 'LR_your first name.py', or 'LR your first name.ipynb', or 'LR your first name.txt' to Avenue-to-Learn (assignment folder of 'Midterm Portfolio') together with this WORD document.