### Regression Analysis for Restaurant RatingsA magazine collected the ratings for food, decor, service, and the cost per person for a sample of 30 restaurants. They combined these ratings to produce a summated rating and used it to predict the cost of a restaurant meal. The data are modeled by:\[\hat{Y}_i = -15.8344 + 0.9901X_i\]where $ X_i $ is the summated rating and $ \hat{Y}_i $ is the meal cost. Perform a residual analysis for these data. Evaluate whether the assumptions of regression have been seriously violated.**Data Table:** Click the icon to view the data table.---### Assumptions EvaluationWhich of the assumptions of regression, if any, have been seriously violated? Select all that apply:- **A.** The assumption of normality has been violated because the normal probability plot does not appear to be a straight line.- **B.** The assumption of independence of errors has been violated because the errors are not independent of one another.- **C.** The assumption of linearity has been violated because the data are clearly curvilinear.- **D.** The assumption of equal variance has been violated because the variability of the residuals is not constant for all values of X.- **E.** The assumptions of linearity, independence, normality, and equal variance do not appear to have been seriously violated.---**Explanation of Graphs/Diagrams:**There are no specific graphs or diagrams shown in the image provided. However, a description of how residuals, normal probability plots, and scatter plots could be used to assess these assumptions in a typical dataset is relevant. - **Residual Plot:** To check equal variance and independence, you would look for a random scatter of points.- **Normal Probability Plot:** To assess normality of residuals, you would look for points that form an approximately straight line.- **Scatter Plot of Fitted Values:** Used to evaluate linearity; a straight pattern supports linearity.Such analyses help determine if the model assumptions are met, ensuring valid inference from the regression model. **Restaurant Data Analysis**This dataset provides a comparison of summated ratings and meal costs across 30 different restaurants. Two primary columns are included:- **Summated Ratings (X):** This column represents the combined evaluation scores for each restaurant.- **Meal Cost (Y):** This column lists the cost of a meal at each restaurant.Here is the data presented:| Restaurant | Summated Ratings (X) | Meal Cost (Y) ||------------|----------------------|---------------|| 1 | 62 | 47 || 2 | 53 | 34 || 3 | 58 | 25 || 4 | 75 | 72 || 5 | 58 | 43 || 6 | 57 | 40 || 7 | 61 | 54 || 8 | 63 | 64 || 9 | 60 | 37 || 10 | 70 | 64 || 11 | 53 | 37 || 12 | 57 | 54 || 13 | 67 | 42 || 14 | 62 | 34 || 15 | 58 | 28 || 16 | 64 | 47 || 17 | 60 | 48 || 18 | 49 | 37 || 19 | 63 | 56 || 20 | 62 | 45 || 21 | 73 | 49 || 22 | 53 | 35 || 23 | 58 | 36 || 24 | 59 | 41 || 25 | 76 | 50 || 26 | 49 | 36 || 27 | 49 | 39 || 28 | 68 | 52 || 29 | 56 | 32 || 30 | 66 | 48 |**Analysis Overview:**- The highest summated rating

Answered: Image /qna-images/answer/0061ada8-dfc1-43aa-8881-3801a7e59aaf.jpg

Answered: A magazine collected the ratings for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The General Aviation Manufacturers Association has reported annual flying hours and fuel consumption for airplanes with a single, piston-driven engine as listedin file XR15057. Data are in millions of flying hours and millions of gallons of fuel, respectively. Determine the linear regression equation describing fuel consumption as a function of flying hours, then identify and interpret the slope, the coefficient of correlation, and the coefficient of determination. At the 0.05 level of significance, could the population slope and the population coefficient of correlation be zero? Determine the 95% confidence intervalfor the population slope.(you can see file XR15057 from photo)
The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x 1) and newspaper advertising (x 2). The estimated regression equation was Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 97 6 1.5 91 3 2 95 5 2.5 93 3.5 2.5 96 4 4.3 94 4.5 2.3 95 3.5 4.2 95 4 3.5 ŷ = 82.5 + 2.01 x 1 + 1.26 x 2The computer solution provided SST = 24 and SSR = 22.876. Compute R 2 and R a 2 (to 3 decimals). R 2 R a 2 When television advertising was the only independent variable, R 2 = 0.551 and R a 2 = 0.476. Are the multiple regression analysis results preferable?
Because colas tend to replace healthier beverages and colas contain caffeine and phosphoric acid, researchers wanted to know whether cola consumption is associated with lower bone mineral density in women. The accompanying data lists the typical number of cans of cola consumed in a week and the femoral neck bone mineral density for a sample of 15 women. Complete parts (a) through (d) below. Click the icon to view the women's data. (a) Find the regression equation treating cola consumption per week as the x-variable. y=x+ (Round to three decimal places as needed.) (b) Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. For 0 colas consumed in a week, the bone density is predicted to be (Round to three decimal places as needed.) g/cm³. OB. For every cola consumed per week, the bone density decreases by (Round to three decimal places as needed.) g/cm³, on average. OC. For a bone density of 0 g/cm³, the number of colas…
A real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (X3). The following table shows a portion of the regression results. ANOVA Significance df SS MS F F gression Residual 3 5694717 1898239 50.88 4.99E-13 36 1343176 37310 Total 39 7037893 Standard Upper 95% Coefficients Error t Stat p-value_Lower 95% Intercept 300 84.0 3.57 0.0010 130.03 470.79 Bed 226 60.3 3.75 0.0006 103.45 348.17 Bath 89 55.9 1.59 0.1195 -24.24 202.77 Sqft 0.2 0.09 2.22 0.0276 0.024 0.39 What would be the rent for a 1000-square-foot apartment that has 2 bedrooms and 2 bathrooms? $840 $1,335 $1,130 $1,260
The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years. Construct and interpret a 98% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $878.The equation of the regression line is y=1.342x+55.816. Wages [state]- 712, 746, 786, 803, 841, 879, 918, 926, 954, 979 Wages [federal]- 1,024, 1,048, 1,098, 1,135, 1,195, 1,240, 1,270, 1,299, 1,340, 1,376 Construct and interpret a 98% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $878. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) PICK THE CORRECT ANSWER [A] We can be 98% confident that when the average weekly wages of state government employees is $878, the average weekly wages of…
For the provided data, develop a regression model for overall satisfaction as a function of years of service and department that has the largest R. Note that the categorical variable department has multiple levels and will require the use of multiple dummy variables. Which department, if any, has the highest impact on roduction satisfaction? Production Production E Click the icon to view the job satisfaction data. Determine the regression model for overall satisfaction as a function of years of service and department that has the largest R. Let "Administrative" be the baseline department, let X, represent Maintenance, let X, represent Management, let X, represent Production, let X, represent Quality Control, and let Xg represent Shipping / Receiving, coding each department variable with a 1 if the person is in that department and 0 otherwise. In addition, let Xe represent Years. Enter the terms of the equation so that the X-values are in ascending numerical order by base. Select the…
The sweetness, y, of the fruit is supposed to be related to the average daily sunshine hours, x. The following data shows the sweetness of the same type of fruit at different locations (sunshine hours). Fit the data to a simple linear regression model. x: 5, 6, 7, 6, 6, 8, 7, 5. y: 9, 10, 10, 11, 12, 13, 12, 8. Predict the true mean sweetness for average daily hours of 8 hours, and calculate the residual for average daily sunshine hours of 8 hours.
Increase in sales (percent) An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (in millions of dollars) and the resulting percentage increase in sales following the campaign, were presented by the firm. Based on these data, we would compute the least-squares regression line to be y = 6.16+0.18x, with x representing campaign cost and y representing the resulting percentage increase in sales. (This line is shown below, along with a scatter plot of the data.) Increase in sales, y Campaign cost, x (in millions of dollars) (percent) 3.02 6.91 7.2+ 1.92 6.80 3.83 6.85 6.8- 1.40 6.37 6.6 - 3.12 6.42 3.56 6.82 6.4- 4.06 6.94 6.2 1.64 6.56 6- 2.06 6.50 1.62 6.18 1.5 2.5 3.5 6.66 Campaign cost (in millions of dollars) 2.87 2.25 6.61 Send data to calculator Based on the firm's data and the regression line, complete the following. (a)…
The applet displays a scatterplot with the following points: (7,10),(27,35),(24,25),(8,12),(10,19),(15,22). Identify the slope of the regression line, intercept of the regression line, and correlation coefficient. Report your answers accurate to within two decimal places.
Using a sample of recent university graduates, you estimate a simple linear regression using initial annual salary as the dependent variable and the graduate's weighted average mark (WAM) as the explanatory variable. If the regression model has an estimated intercept of 3200 and an estimated slope coefficient of 550, what is the predicted starting salary of a student with a WAM of 64?
Listed below are paired data consisting of movie budget amounts and the amounts that the movies grossed. Find the regression equation, letting the budget be the predictor (x) variable. Find the best predicted amount that a movie will gross if its budget is $130 million. Use a significance level of α=0.05. A. The regression equation is Y= (Round to one decimal place as needed.) B. The best predicted gross for a movie with a $130 million budget is $ million. (Round to one decimal place as needed.)
The datasetBody.xlsgives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (lb), Height (in), and circumference (cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. We are interested in predicting body fat based on abdomen circumference. Find the equation of the regression line relating to body fat and abdomen circumference. Make a scatter-plot with a regression line. What body fat percent does the line predict for a person with an abdomen circumference of 110 cm? One of the men in the study had an abdomen circumference of 92.4 cm and a body fat of 22.5 percent. Find the residual that corresponds to this observation. Bodyfat Abdomen 32.3 115.6 22.5 92.4 22 86 12.3 85.2 20.5 95.6 22.6 100 28.7 103.1 21.3 89.6 29.9 110.3 21.3 100.5 29.9 100.5 20.4 98.9 16.9 90.3 14.7 83.3 10.8 73.7 26.7 94.9 11.3 86.7 18.1 87.5 8.8 82.8 11.8 83.3 11 83.6 14.9 87 31.9 108.5 17.3…

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