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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- An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y=nothingx+(nothing) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. A weightless car will get nothing miles per gallon, on average. It is not appropriate to interpret the slope. B. For every pound added to the weight of the car, gas mileage in the city will decrease by nothing mile(s) per gallon, on…A least squares regression line was calculated to relate the length (cm) of newbom boys to their weight in kg. The regression analysis gives the model Weight = -5.11 +0.1952 Length. Complete parts a through c below. O D. For every additional 1 kg of weight, the length of the baby is predicted to increase by 0.1952 mm. b) If a baby is 53 cm long, what is his predicted weight? O kg (Round to two decimal places as needed.) c) Consider a baby boy that was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him? The residual is . (Round to two decimal places as needed.) This means that the baby is kg V than predicted by his length. (Round to two decimal places as needed.)Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x where x is metatarsal-to-femur ratio and y is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct a 96% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. contact us help 6:42 PM povecy polcy terms of use careers A E O 4») 18 -క90.4 58 12/14/2020 a 17 |耳 即 delets prt sc insert 112 19 18 + 16 backspace f5 fA
- estion 7 of 15 Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (°F), as the explanatory variable and the number of ice bags sold on as the response variable. The least squares regression (LSR) line for the data is y = -114.05 +2.17x. On one of the observed days, the temperature was 82 °F and 66 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, ŷ, when the temperature is 82 °F. Enter your answer as a whole number, rounding if necessary. ice bags Using the predicted value you just found, compute the residual at this temperature. residual = ice bags DOLLThe 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 27The following regression model was estimated. Q is the number of meals served, P is the average price per meal (customer ticket amount, in dollars), Rxis the average price charged by competitors (in dollars), Ad is the local advertising budget for each outlet (in dollars), and I is the average income per household in each outlet's immediate service area. Least squares estimation of the regression equation on the basis of the 25 data observations resulted in the estimated regression coefficients and other statistics given in Table below. Variable Coefficient Standard Error of Coefficient Intercept 128832.240 69974.818 Price (P) Competitor Price (Px) | Advertising (Ad) Income () -19875.954 4100.856 15467.936 459.280 0.261 0.094 8.780 1.017 Coefficient of determination R =83.3% (a) Interpret the coefficients of independent variables. (b) Test the significance of independent variables at 5% level of Significance. (c) Interpret R? with the help of adjusted R2. (d) Test for the overall…
- Explain the concept of Linear Regression with Multiple Regressors?Compute the least-squares regression line for predicting the 2012 budget from the 2006 budget. Round the slope and y- intercept to at least four decimal places.In a simple regression, the ordinary least squares estimate of the slope coefficient is expected to be more precise the greater is the variation in the dependent variable and the lesser is the variation in the independent variable. True False
- This was not the correct quadratic model for the dataA 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.…The table lists the average tuition and fees at private colleges and universities for selected years. Year 1985 1990 1995 2000 2008 5311 25,115 Tuition and Fees (in dollars) 9375 SO 12,418 (a) Find the equation of the least-squares regression line that models the data. y 840.450 (Type the slope as a decimal rounded to three decimal places. Round the y-intercept to the nearest integer.) (b) Graph the data and the regression line in the same viewing window using the parameters given below the graph choices. Choose the correct graph below. OA. O B. o HE RO OC. 16,230 A o ƠN