For the data given : -Fit a least squares line to the data. -Plot the data and g
ID: 3437557 • Letter: F
Question
For the data given :
-Fit a least squares line to the data.
-Plot the data and graph the line.
-Calculate r and r2; interpret their values.
-Is the model useful (90% confidence interval) for predicting y?
-Estimate y given x = 10. Use a 90% confidence interval
Y X 58.91917314 17.9441336 13.57450242 6.12632559 29.3510094 12.8002848 45.64305354 15.57287621 -2.648422623 8.695513665 44.06502304 12.80388374 50.20597577 14.24341375 30.07622849 5.649884292 37.53191814 12.02881596 39.98763409 13.4763698 46.96164978 19.19645139 25.60818927 9.168443517 42.66781837 13.52147073 33.77291567 6.092608631 39.12879011 11.56356009 43.07872857 14.30645052 43.51514269 9.524191495 19.97826821 1.344326967 44.85200986 18.00158661 36.10558182 9.339117519 8.74116488 5.553085772 62.22326432 11.92228699 19.10002051 4.344504869 4.429185513 6.03277689 33.18251152 4.634981732 37.69023567 17.93512977 32.82332528 7.377868327 47.79558313 15.74506664 31.4553294 1.182070999 33.75199949 12.46278751 21.86032694 8.275259269 57.83697505 13.76913395 20.31702021 8.661682752 26.10576109 5.95641473 26.73859946 0.082539129 11.46490278 12.56121459 30.5172699 19.83131481 42.65479476 14.86181506 58.11222346 16.9411625 78.01812341 12.94288059 51.01794935 18.95044451 13.87470654 14.55600802 54.42381195 19.23347452 13.21304338 6.226046222 18.18269123 2.14775948 5.081059876 2.040475183 29.01467642 11.42179127 13.78004308 1.962144154 4.037299486 0.557280575 36.08791397 17.42440261 10.82561657 1.535862587 60.75949037 11.86784676 19.2654877 13.26464288 30.71052795 5.894218568 18.28906623 1.723702036 44.0640593 15.24302873 49.28771824 16.84514569 71.7365424 17.6801154 1.591984571 0.024247438 41.25121241 16.64329523 17.70185656 0.979867578 38.63051186 0.762031575 -1.361124256 6.065775263 58.30213707 17.60707338 10.29320205 9.370296876 -12.80911099 0.589688381 63.99814441 15.14417208 39.89835626 11.26539367 29.46070879 9.772175717 26.74835913 6.872940569 12.07361556 11.06240389 25.6395985 7.992690392 21.14998145 4.61432529 20.7040192 1.259273205 36.98005302 14.00887369 0.718428855 3.864104412 28.07984886 12.78772697 30.17861878 9.251116269 90.30933506 18.68362385 -4.52484206 7.165764446 12.941613 3.248634124 42.11788439 8.150724049 51.59458 12.59120492 51.60946033 19.49341114 65.88231016 15.84169803 30.71155647 3.616634255 46.09816083 18.45406965 32.2485384 1.652796065 56.53126019 7.239351102 43.37319811 17.10232366 13.82991967 8.621716957 20.58527511 5.292266003 56.462476 14.62785029 36.2813413 15.16897518 14.05597424 3.870469984 29.26498968 12.70525191 41.37653997 9.339120222 23.19082164 7.864050797 8.636308408 1.909121706 23.70099472 8.285990079 23.97055423 11.4312186Explanation / Answer
The equation of the line best fit is given as:
Y = 2.2755 X + 9.5767
R = 0.67772
R2 = 0.4593
The values of R and R2 are pretty low. So, the model is not very accurate in predicting. the R2 determines the amount of regression explained by this line.
For X = 10, we have the predicted value of Y as:
Y-hat = (2.2755 * 10) + 9.5769
= 32.331
Hope this helps. Refer to the table for p-values and other statistics
Y X 58.91917314 17.94413360 SUMMARY OUTPUT 13.57450242 6.12632559 29.35100940 12.80028480 Regression Statistics 45.64305354 15.57287621 Multiple R 0.677728855 -2.64842262 8.69551367 R Square 0.459316402 44.06502304 12.80388374 Adjusted R Square 0.453854951 50.20597577 14.24341375 Standard Error 14.20313791 30.07622849 5.64988429 Observations 101 37.53191814 12.02881596 39.98763409 13.47636980 ANOVA 46.96164978 19.19645139 df SS MS F Significance F 25.60818927 9.16844352 Regression 1 16965.73 16965.73 84.10154 7.04E-15 42.66781837 13.52147073 Residual 99 19971.18 201.7291 33.77291567 6.09260863 Total 100 36936.91 39.12879011 11.56356009 43.07872857 14.30645052 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% 43.51514269 9.52419150 Intercept 9.57669929 2.841302 3.370533 0.001071 3.938941 15.21446 4.859027 14.29437 19.97826821 1.34432697 X 2.275473326 0.248125 9.170689 7.04E-15 1.78314 2.767806 1.863489 2.687457 44.85200986 18.00158661 36.10558182 9.33911752 8.74116488 5.55308577 62.22326432 11.92228699 19.10002051 4.34450487 4.42918551 6.03277689 33.18251152 4.63498173 37.69023567 17.93512977 32.82332528 7.37786833 47.79558313 15.74506664 31.45532940 1.18207100 33.75199949 12.46278751 21.86032694 8.27525927 57.83697505 13.76913395 20.31702021 8.66168275 26.10576109 5.95641473 26.73859946 0.08253913 11.46490278 12.56121459 30.51726990 19.83131481 42.65479476 14.86181506 58.11222346 16.94116250 78.01812341 12.94288059 51.01794935 18.95044451 13.87470654 14.55600802 54.42381195 19.23347452 13.21304338 6.22604622 18.18269123 2.14775948 5.08105988 2.04047518 29.01467642 11.42179127 13.78004308 1.96214415 4.03729949 0.55728058 36.08791397 17.42440261 10.82561657 1.53586259 60.75949037 11.86784676 19.26548770 13.26464288 30.71052795 5.89421857 18.28906623 1.72370204 44.06405930 15.24302873 49.28771824 16.84514569 71.73654240 17.68011540 1.59198457 0.02424744 41.25121241 16.64329523 17.70185656 0.97986758 38.63051186 0.76203158 -1.36112426 6.06577526 58.30213707 17.60707338 10.29320205 9.37029688 -12.80911099 0.58968838 63.99814441 15.14417208 39.89835626 11.26539367 29.46070879 9.77217572 26.74835913 6.87294057 12.07361556 11.06240389 25.63959850 7.99269039 21.14998145 4.61432529 20.70401920 1.25927321 36.98005302 14.00887369 0.71842886 3.86410441 28.07984886 12.78772697 30.17861878 9.25111627 90.30933506 18.68362385 -4.52484206 7.16576445 12.94161300 3.24863412 42.11788439 8.15072405 51.59458000 12.59120492 51.60946033 19.49341114 65.88231016 15.84169803 30.71155647 3.61663426 46.09816083 18.45406965 32.24853840 1.65279607 56.53126019 7.23935110 43.37319811 17.10232366 13.82991967 8.62171696 20.58527511 5.29226600 56.46247600 14.62785029 36.28134130 15.16897518 14.05597424 3.87046998 29.26498968 12.70525191 41.37653997 9.33912022 23.19082164 7.86405080 8.63630841 1.90912171 23.70099472 8.28599008 23.97055423 11.43121860