\f+1 cys_acid 23x1 double 2 1 4.3900 2 4.3000 3 4.2700 4 4.3300 5 4.0100 6 3.9900 3.9700 8 3.8200 3.9300 10 3.8100 11 3.5400 12 3.7200 13 3.6500 14 3.1200 15 1.8700 16 1.4900 17 1.5300 18 1.3200 19 1.2100 20 1.1900 21 1.2200 22 1.0300 23 0.8800Data for Part 2 is contained in the attached data le carpet_data.mat. The variables in the MAT file are the following: o cys_acid: cysteic acid content, unit grams of cysteic acid. 0 age: age of carpet, unit years (as in \"years old") For any questions requiring an answer to be reported in a sentence, be sure to use complete sentences. Points will be deducted for incomplete sentences. Plots must be legible in the Word doc. Plots that don't follow all plotting instructions will lose points. 1. Plot the experimental data (5 points) . Make a scatter plot of the carpet measured age (yr, response variable) vs. cysteic acid content (Xi, predictor variable). 0 Use blue circle markers of marker size 50 if using the scatter function. Use marker size 10 if using the plot function. 0 Set the font size of all numbers and text in the gure to be size 16. 0 Label the axes with the quantity and their units. o Do not include lines between the marker points, just plot the data set as discrete points. 2. Linear regression model (15 points) Assuming that a simple linear regression model is appropriate, t the regression model relating cysteic acid content (Xi, predictor variable) to the wool carpet age (yr, response variable). 0 Use the following table to arrive at the linear regression model for these data. a An editable version of the table is in the attached Word docx le under this Pro'eot Blackboard item. \" Linear regression A 3': = x+ model 5?: = 131x.- + 0 3. Visualize the linear regression model (5 points) 0 On the same gure you made in Step 1 (use hold on), plot the linear regression line 3"): = 3196: + 30. 0 Plot the regression line as a red solid line of line width 2. o This line should look continuous and span the entire domain of the original data set. 0 Save this plot as a jpg or png le and include it in your Project 5 answers document. 4. What change in carpet age (in years) is expected when the amount of cysteic acid changes by +1 9 cysteic acid? Report your answer as a complete sentence. (5 points) 5. Calculate the expected value of j? forx = 3.81 g cysteic acid and the corresponding residual (enor). Report and interpret your answers in complete sentences. You must use the phrases \"prediction from the best-t line\" and \"experimental measurement\" in your response for full credit. (10 points)