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- EXER 5.1: Given the observations (1,1), (2,3), (4,5), find the least squares estimates for m and b for the best fit line y=mx+b.3. Fit a least squares quadratic curve to the following data and estimate Y at X = 2.4 fig. 03 2 3. 4. గోలిగౌజి రర్ Y 1.7 1.8 2.3 2.3 A. The required least squares quadratic curve(parabola) and the estimated value of Y at X=2.4? * 大 O Y= 2- 0.5X + 0.2X^2; Y = 1.952 Y= 2-0.6X+ 0.2X^2; Y = 1.712 O Y= 2.1 - 0.5X + 0.2X^2;Y = 2.052 Y= 2- 0.5X + 0.4X^2; Y = 3.104When a least squares line is fit to the 11 observations in the service time data, we obtain SSE = 334.1354. Calculate s and s. (Round s2 to 4 decimal places. Round s to 5 decimal places.)
- Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. SSE a. Let x equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables (to 2 decimals). + 1.59 b. Test whether revenue and advertising expenditures are related at a 0.05 level of significance. Compute the following (to 2 decimals). SST SSR MSR 30.21 x X MSE Compute the F test statistic (to 2 decimals). Advertising Expenditures What is the p-value? Use Table 4 from Appendix B. between 0.01 and 0.025 1 2 4 6 10 14 20 Revenue 20 32 45 40 53 54 55Use the data in vapor.csv, obtain the transformed predictor 1/X, and the transformed response log(Y), where "log" refers to the natural logarithm. Denote the new predictor by X*(=1/X) and denote the new response by Y*(=log Y). Fit a least squares model for the new response and the new predictor. It turns out that the estimated intercept is [ PUT ANSWER HERE ] , and the estimated slope is[ PUT ANSWER HERE ] . The estimated standard error of the estimated slope is [ PUT ANSWER HERE ] , and the value of the F statistic associated with this fitted model is equal to [ PUT ANSWER HERE ]. Note: The data in vapor.csv is attached as an imageThe following data shows the atmospheric pollutants yi(relative to an EPA standard) at half hour interval xi. Find the equation y=a+bx of the least square line that best fits the data points given by 2,1, 5,2, 7,3, 8,3. Hence predict the atmospheric pollutant at x=6 half hour.
- The defending attorney Mr. Justin Case was interested in how a lengthy trial could affect howlong a jury would deliberate on a case (and see if he should just cut to the chase). He observed asample of courtroom trials and noticed the following:Days inTrial (X) 5 2 6 4 5 6 2 4 2 1 HoursDeliberation (Y) 4 4 1 3 1 3 9 2 3 7 5) Mr. Case’s client’s most recent case took 10 days to complete. How long should he \ predict the jury deliberation will take?3. An economist used the least squares procedure to fit a regression model of the form y₁ = B₁ + B₁x₁, +B₂x2, +,, where y is quantity demanded of a good (in million units), x, is price of the good (in cedis), x₂ is household income (in thousand cedis), and E, ~ N (0,0¹). Tabulated below are sums obtained 8 sets of observations Σ.y=483 2y =30567 Ex₁y=3068 Σχ =53 Σχ = 365 Σx₂y=3795 Calculations have produced the following matrix (x'x)' = 50.68462 -4.03077 0.33846 Ex=60 Σ.x = 472 Σxx, = 382 -3.18077] 0.23846 0.21346 a. Form the matrices: XX and X'Y. b. Use (X'X) and X'Y to compute the OLS estimates for B₁, i = 0,1,2. c. Write the fitted regression model and interpret the partial regression coefficients.A certain experiment produces the data (1,7.9), (2,5.4), and (3, –.9) · Describe the model that produces a least-squares fit of these points by a function of the form y = A cos x + B sin x
- When a least squares line is fit to the 12 observations in the labor cost data, we obtain SSE =656, 214.3589. Calculate s2 and s (isnt n-k-1)?Agla) d 45 as 52 diall Al Jlas ala Estimate a,b of regression ine for the folowing data: O - 10, Ex, - 2017.9, Ey, - 1574.8 Exy, - 222657 88, Ex',- 5949.85, Ey',- 124039.58 a= 72.96 ,b = 0.041 g= -12.2 ,b= 2.21 None co a= 12.96 ,b= 141.0 25 a 16 Jull ll a ha a J JA po9. Differentiate y = Vsec3 (5t2)