The following data is given: 3 4 14 12 9 _y 4 7 11 Use linear least-squares regression to determine the coefficients m and b in the function y mx + b that best fit the data. Use Eq. (6.5) to determine the overall error.
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A: Giventhe least square regression equation is y=28.77+0.3467(x)The value of x is 35
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- Based on the data presented in the table below, please calculate the values of b0 and b1 using OLS (ordinary least squares) and for the equation: q1 = β0 + β1pi + ui. qi pi 1 2 2 3 3 5The 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…A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…
- An airline developed a regression model to predict revenue from flights that connect "feeder" cities to its hub airport. The response in the model is the revenue generated by flights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air distance between the hub and feeder city (Distance, in miles) and the population of the feeder city (in thousands). The least squares regression equation based on data for 37 feeder locations last month is Estimated revenue = 81 +0.3Distance + 1.4Population with R² = 0.75 and so = 31.2. Complete parts a through d. (a) The airline plans to expand its operations to add an additional feeder city. The first possible city has population 150,000 and is 275 miles from the hub. A second possible city has population 180,000 and is 250 miles from the hub. Which would you recommend if the airline wants to increase total revenue? The first city The second cityThe marketing manager wants to estimate the effect of the MBA program on Salary controlling for the other factors. Which regression model is the MOST appropriate? Oa. Salary = B_0+B_1 MBA + ε Ob. Salary = 3_0+ B_1 MBA + B_2 Work + e c. Salary = B_0+B_1 MBA+B_2 Work + B_3 Age +8 Od. Salary = B_0+ B_1 MBA + B_2 Work + B_3 Age +B_4 Gender + εFit the function y = A xB by the method of least squares
- Do not show any work on this question. For these ordered pairs: (0, 0.1), (1, 1), (2,2.4),(4,3.7), and (5, 5.7): Find (f ,y) and plot it as well as the five given points. Find the equation ofthe least squares regression line. Round off the x coefficient and the constant to the nearest onethousandth. Graph the equation together with the points above. If needed do not use a Pvalue to answer any problem. No credit will be given if a P value is used. Use only criticalvalues.please show workThe table shows the number of goals allowed and the total points earned (2 polnts for a win, and 1 point for an overtme or shootout loss) by 14 lce hockey teams over the course of a season The equation of the regression line is (a) Find the coefficient of determination,, and interpret the result (b) Find the standard error of the estimate, and interpret the resut Goals Allowed, x Points, y -0.560x 218.067 Use he data to answer the folowing questions 217 213 221 229 260 262 277 205 216 20s 217 208 257 246 66 70 105 105 0 83 47106 103 97 9182 91 88 Inco (a) r-O (Round to three decimal places as noeded.)
- 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…The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x₁) and newspaper advertising (x₂). The estimated regression equation was ŷ = 83.5+ 2.21x₁ + 1.80x₂. The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.495. (a) Compute and interpret R² and R2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R² = 0.653 and R2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis ---Select--- preferred since both R² and R2 show ---Select--- ✓percentage of the variability of y explained when both independent variables are used. . Adjusting for the number of…
