The following standardization data were provided for a series of external standards of Cd²+ that had been buffered to a pH of 4.6.
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- Calculate the R2of the following multivariate sample regression functions and interpret theanswers.3.1 Investment-hat = β1-hat + β2-hat*Interest rate + β3-hat*Exchange rateESS = 900RSS = 1003.2 Investment-hat = β1 + β2-hat*Interest rate + β3-hat*number of 311 studentsESS = 400RSS = 6003.3 Salary-hat = β1 + β2-hat*Frequency of blinking eyes + β3-hat*Colour of hairRSS = 950TSS = 1000The following data shows the dexterity test scores of five assembly-line employees of Dimples Company Limited and their respective hourly productivity.Employee Score on dexterity test (?) Ali 12Kofi 14Kwesi 17Abudu 16Nana 11Units produced in an hour (?) 55636770 51You are required to(i) Write the regression equation(ii) Interpret the regression equation(iii) Calculate the Pearson’s Product Moment Correlation Coefficient.(iv) Interpret the correlation coefficient (v) Suppose the dexterity test score is 13, what would be the units produced in an hour? (vi) Clearly explain (in detail) the difference between regression analysis and correlation analysis.Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73520.7352 R Square 0.54050.5405 Adjusted R Square 0.52050.5205 Standard Error 2131.18202131.1820 Observations 4949 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 245,793,126.4218245,793,126.4218 122,896,563.2109122,896,563.2109 27.058227.0582 1.7E-081.7E-08 Residual 4646 208,929,085.5374208,929,085.5374 4,541,936.64214,541,936.6421 Total 4848 454,722,211.9592454,722,211.9592 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14268.6823614268.68236 2,521.08442,521.0844 5.65975.6597 0.0000009340.000000934 9194.00279194.0027 19,343.362119,343.3621 Education (Years) 2352.26982352.2698 337.1115337.1115 6.97776.9777 0.000000010.00000001 1673.69951673.6995 3030.84013030.8401 Experience (Years) 832.2096832.2096…
- Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73360.7336 R Square 0.53810.5381 Adjusted R Square 0.51800.5180 Standard Error 2140.27632140.2763 Observations 49 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 245,430,999.7671245,430,999.7671 122,715,499.8836122,715,499.8836 26.789226.7892 1.9E-081.9E-08 Residual 4646 210,716,007.0084210,716,007.0084 4,580,782.76114,580,782.7611 Total 4848 456,147,006.7755456,147,006.7755 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14276.146814276.1468 2,531.84252,531.8425 5.63865.6386 0.0000010040.000001004 9179.81229179.8122 19,372.481419,372.4814 Education (Years) 2349.95952349.9595 338.5500338.5500 6.94126.9412 0.0000000110.000000011 1668.49371668.4937 3031.42533031.4253 Experience (Years) 833.6183833.6183…Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73360.7336 R Square 0.53810.5381 Adjusted R Square 0.51800.5180 Standard Error 2140.27632140.2763 Observations 49 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 245,430,999.7671245,430,999.7671 122,715,499.8836122,715,499.8836 26.789226.7892 1.9E-081.9E-08 Residual 4646 210,716,007.0084210,716,007.0084 4,580,782.76114,580,782.7611 Total 4848 456,147,006.7755456,147,006.7755 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14276.146814276.1468 2,531.84252,531.8425 5.63865.6386 0.0000010040.000001004 9179.81229179.8122 19,372.481419,372.4814 Education (Years) 2349.95952349.9595 338.5500338.5500 6.94126.9412 0.0000000110.000000011 1668.49371668.4937 3031.42533031.4253 Experience (Years) 833.6183833.6183…The following is a partial computer output of a multiple regression analysis of a data set containing 20 sets of observations on the dependent variableThe regression equation isSALEPRIC = 1470 + 0.814 LANDVAL + 0.820 IMPROVAL + 13.5 AREA Predictor Coef SE Coef T P Constant 1470 5746 0.26 0.801 LANDVAL 0.8145 0.5122 1.59 0.131 IMPROVAL 0.8204 0.2112 3.88 0.0001 AREA 13.529 6.586 2.05 0.057 S = 79190.48 R-Sq = 89.7% R-Sq(adj) = 87.8% Analysis of Variance Source DF SS MS Regression 3 8779676741 2926558914 Residual Error 16 1003491259 62718204 Total 19 9783168000 For the problem above, we want to carry out the significance test about the coefficient of LANDVAL, what is the t-value for this test, and is it significant? 46.66, significant 2.05, significant 1.59, not significant 0.26, not significant
- Consider the following computer output from a multiple regression analysis relating the price of a used car to the variables: age of car, mileage, and safety rating. Coefficients Coefficients Standard Error t� Stat P-value Intercept 42465.6942465.69 5320.545320.54 7.9817.981 0.00000.0000 Age (Year) −21096.02−21096.02 2551.522551.52 −8.268−8.268 0.00000.0000 Mileage(in Thousands) −1312.73−1312.73 103.02103.02 −12.743−12.743 0.00000.0000 Safety Rating 1533.821533.82 165.72165.72 9.2559.255 0.00000.0000 Does the sign of the coefficient for the variable safety rating make sense?Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.consider the coefficient estimates of the following market model linear regression of general motors (gm) on the S&P500 market returns coefficient estimate std error tvalue pr(>ItI) intercept 0.005860 0.0003704 1.582 0.12412 sp500 0.0904753 0.266702 3.392 0.00196 The number of observations is 32.At the 1% significance level, what is the (1)test statistic value,(2) the critical values (3) decision regarding the null hypothesis that the beta coefficient on the market returns is equal to 1.61
- The Road Department is trying to see whether they should buy road treatments ( in tons) for storms based on the number of inches of snow for each recorded. Use Pearson r at alpha- 0.05 to test the hypothesis. ILLUSTRATE THE NORMAL CURVE inches in snow 1.5 1.7 3.7 2.8 4.6 2.4 3.1 2.9 3.6 4.2 3.1 number of tons 805 905 1235 1000 1302 998 1102 1305 1456 1600 1005table 7 autocorrelations of the residuals from estimating the regression ΔgPMt = 0.0006 − 0.33301 ΔgPMt −1 + εt 1Q:1992–4Q:2001 (40 Observations) regression Statistics R-squared Standard error Observations Durbin–watson intercept ΔgPMt −1 ΔgPMt −4 Coefficient −0.0001 −0.0608 0.8720 0.9155 0.0057 40 2.6464 Standard error 0.0009 0.0687 0.0678 t-Statistic −0.0610 −0.8850 12.8683 lag 1 2 3 4 5 autocorrelation −0.1106 −0.5981 −0.1525 0.8496 −0.1099 table 8 shows the output from a regression on changes in the gPM for home Depot, where we have changed the specification of the ar regression. table 8 Change in gross Profit Margin for home Depot 1Q:1992–4Q:2001 a. identify the change that was made to the regression model. b. Discuss the rationale for changing the regression specificationThe following output was obtained from a multiple regression analysis. Analysis of variance SOURCE DF SS MS Regression 5 100 20 Residual Error 20 40 2 Total 25 140 Predictor Coefficient SE Coefficient t Constant 3.00 1.50 2.00 x1 4.00 3.00 1.33 x2 3.00 0.20 15.00 x3 0.20 0.05 4.00 x4 −2.50 1.00 −2.50 x5 3.00 4.00 0.75 Conduct a global test of hypothesis H0: β1 = β2 = β3 = β4 = β5 = 0; H1: Not all β's are 0 at the 0.05 significance level. d-1. State the decision rule. (Round your answer to 2 decimal places.) Reject H0 if F> d-2. What is the computed value of F? (Round your answer to 1 decimal place.) Value of F d-3. Determine whether any of the regression coefficients are significant. ----------------Reject H0 Atleast One regression Coefficient is---------------- Accept Zero…