Linear Regression is applied for a supervised learning problem with a training dataset with m-110 observations. The training dataset records, for each observation, n=8 input features, as well as one output. The total sum of squares (TSS) is 402. The residual sum of squares (RSS) is 345. Compute the F-ratio of the model.
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- The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature ( x1 ), the number of days in the month ( x2 ), the average product purity ( x3 ), and the tons of product produced ( x4 ). The past year’s historical data are available and are presented in the following table:regression model is y = -102.7132 + 0.6054X1 + 8.9236X2 + 1.4374 X3 + 0.0136X4 a) Estimate sigma^2b.) Using ANOVA, test for significance of regression using α=0.05. Determine the critical value of the test statistic (2 decimal places only). c.) Using ANOVA, test for significance of regression using α=0.05. Determine the computed value of the test statistic d) Calculate R^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %). e) Calculate R_adj^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %).f) Test the significance of x3 at α=0.05. Determine the value of the test statistic. g)…Find the least-squares regression line treating square footage as the explanatory variable. y = (Round the slope to three decimal places as needed. Round the intercept to one decimal place as needed.)The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 43.875. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. Weight |(pounds), x Miles per Gallon, y Car 1 3,770 20 Car 2 3,980 19 Car 3 3,530 19 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,729 20 Car 7 2,607 26 Car 8 3,776 19 Car 9 3,311 22 Car 10 2,999 27 Car 11 2,755 27
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- A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight=−5.59+0.1826 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him?For a linear regression problem, The actual observed y-value when x = 2 is y = 6. The least squares line is y = 2x+1. The predicted value when x=2 is y = 5. Determine the value of the residual (prediction error) oooo 1 6 5 Cannot be determined from the information givenA physics student wants to measure the stiffness of a spring (force required per cm stretched). He knows that according to Hooke's law, there is a linear relationship between the distance a spring is stretched and the force needed to stretch the spring. He collects some data by measuring the force applied to the spring when he stretches the spring by some amount. The plot and the least squares fit is given below.From the regression model, the intercept was found to be -2.532 and the slope was found to be 25.321.Part i).The stiffness of the spring was predicted to beA. -9.961B. 25.321C. 50.642D. -2.532E. 125.84Part ii).Refer to the previous question, the physics student used the regression model to predict that a force of 377.28N would be required to stretch the spring by 15cm. Remarkably, his prediction was horribly wrong. Can you explain why? (Check all that apply)A. He made a prediction outside of the range of forces observed.B. He had outliers or influential points in his data.C.…
- A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight = -5.25 +0.1696 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him?A statistics student is studying if there is a relationship between the price of a used car and the number of miles Using the computer output, what is the equation of the least-squares regression line? it has been driven. She collects data for 20 cars of the ý = -0.181 + 24157.2x same model with different mileage, and determines each car's price using a used car website. The analysis is ý = 24157.2 -0.181x given in the computer output. ý = 2164.1 + 0.024x Predictor Coef SE Coef t-ratio Oŷ = 0.024 + 2164.1x Constant 24157.2 2164.1 2.965 0.046 Mileage -0.181 0.024 5.377 0.000 S 3860.7 R-Sq = 68.0% R-Sq(Adj) = 67.5%An article gave a scatter plot, along with the least squares line, of x = rainfall volume (m³) and y data on rainfall and runoff volume (n = runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to 15) given below. The equation of the least squares line is y = -2.364 + 0.84267x, ² 0.976, and s = 5.21. = x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101 (a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal places.) Ŷ 28.25 1x ) m³ Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. OYes, precise information is available because the resulting interval is very wide. 34.46 Yes, precise information is available because the resulting interval is very…