Question

The horsepower (Y, in bhp) of a motor car engine was measured at a chosen set of values of running speed (X, in rpm). The data are given below (the first row is the running speed in rpm and the second row is the horsepower in bhp): 1100 1400 1700 2300 2700 3200 3500 4000 4300 4600 4900 5200 6100 Horsepower (bhp) 53 62.39 81.64 102.55 142.01 154.47 165.35 182.59 204.22 216.1 250.14 251.66 312.52 The mean and sum of squares of the rom are 3461.5385 rpm and 185040000.0000 rpm 2 respectively; the mean of the horsepower values is 167.5877 bhp and the sum of the products of the two variables is 9020011.0000 rpm bhp. A scatterplot displaying the data is shown below: rpm Car Engine Horsepower against Engine Running Speed 0 006 250 o a 200 Horsepower (p) 150 100 50 T 2000 1000 3000 4000 5000 8000 Engine running speed (rpm) Please provide answers to the following to 3 decimals places where appropriate: Parta) Compute the regression line for these data, and provide your estimates of the slope and intercept parameters. Please round intermediate results to 6 decimal places. Slope: Intercept:

Answer 1

From a a give example we have x = 3461.5385 Epi-p12 - 18 50 40 000 0000 rpm? y = 167.5877 ECRi-de) (Li-y) = 902ool1.000 rpm 6hp n=13 Now Partal where a and Now we know that y=a+bre be the equation of line or regression yon b are obtained by the method of least square by minimizing the enor sum of square a= y - 6 and 5 = 2( - 2) (8i - 4) Eli-ze)? go zooll.oooo 1850 40000 0000 0.048746 a = 167.5877- (0.048746 X 3461.5385) -1.148456 Equation of line of regression you do is y = (0.048746) 3 - 1.148456 slope = b = 0.048746 intercept = a = d = -1.148456 CS Scanned with CamScanner

DRTE Part 6) Here want to find horsepower when we 2uoo equation, we put x-2400 to the regression get y = (0.049 x 2400) - 1.148 116.452 100 116.452 the level of horsepower would we expect the engine produce is running 2000 rpm part As we know the regression coefficient slope are independent of change of origin but depends on the change change of scale Here increase the rpm by hence horsepower also chango with respect to the rpm because here change the scale calculate the predicted value of rpm 9 - the Now if we increase rpm by loo then horsepower become ġ = (o.oug x2600') - 1.148 from part 6) 2400 116.452 rpm = 2500 121.352 CS Scanned with CamScanner

DATE From given by above calculation rpm is increased then horsepower is increase by 121352 - 116.452 - 4.9 partd) It is will by 4.9 we know loo(1-2% confidence interval for slope is given by (6- tn.242 se (6) se (6) bttn-2, az Here th-222 = 21a- oos e til 0.025= 2.201 2 secbl=0.001543 upper bound 6t tn-2al2 sel 6) of 0.049 + ( 2.201 x 0.001543) 0.0 52 b- tn.2.212 se (6) lower bound of cI 0.049 - 02.201 x 0.001543) 0.0 46 go do confidence interval for slope is given as (0.046 0.052) CS Scanned with CamScannen

t table as follows:

7:43 62.0 KB/S 774 Edit 26 Х t-distribution Confidence Level 85% 90% 95% 98% 60% 70% 80% 99% 99.8% 99.9% 2 Tailed 1 Tailed 0.40 0.20 0.30 0.15 0.20 0.10 Level of Significance 0.15 0.10 0.05 0.02 0.075 0.05 0.025 0.01 0.01 0.005 0.002 0.001 0.001 0.0005 26.30 12.39 8.499 6.835 5.946 5.403 5.039 0.039 4.780 2.822 3.250 df 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 18 19 20 21 22 23 24 25 4.586 4.437 1.376 1.963 3.133 4.195 6.320 12.69 31.81 63.67 1.060 1.385 1.883 2.278 2.912 4.271 4.271 6.816 9.520 0.978 1.250 1.637 1.924 2.352 3.179 4.525 5.797 0.941 1.190 1.533 1.778 2.132 2.776 3.744 4.596 0.919 1.156 1.476 1.699 2.015 2.570 3.365 4.030 0.906 1.134 1.440 1.650 1.943 2.447 3.143 3.707 0.896 1.119 1.415 1.617 1.895 2.365 2.999 3.500 0.889 1.108 0.00% 1.397 1.592 1.860 2.306 2.897 3.356 0.000 0.883 1.100 1.383 1.574 1.833 2.262 0.879 1.372 1.093 V. 1.559 1.813 2.228 2.764 3.170 0.875 0.00 1.088 1.363 1.305 1.548 1.796 2.201 2.719 3.106 0.873 1.083 1.356 1.538 1.782 2.179 2.682 3.055 0.870 1.079 1.350 1.530 1.771 2.160 2.651 3.013 0 000 0.868 1.076 1.345 1.523 1.761 . 15 2.145 2.625 2.977 0.866 1.074 1.341 1.517 1.753 2.131 2.603 2.947 0.865 1.071 1.337 1.512 1.746 2.120 2.584 2.921 0.863 1.069 1.333 1.508 1.740 2.110 2.567 2.899 0.862 1.067 1.330 1.504 1.734 2.101 2.553 2.879 0.861 1.000 1.066 1.328 1.500 1.000 1.729 2.095 2.093 2.540 2.861 0.860 1.064 1.325 1.497 19 1.725 .125 2.086 2.529 2.840 0.859 1.063 1.323 1.494 1.721 2.080 2.518 2.832 0.858 1.061 1.321 1.717 2.074 2.074 2.509 2.819 0.857 1.060 1.319 1.489 1.714 2.069 2.500 2.808 0.857 1.487 1.711 2.064 2.493 2.797 0.856 1.058 1.485 1.708 2.060 2.486 2.788 0.856 1.058 1.315 1492 1.483 1.706 2.056 2.479 2.779 0.855 1.057 1.314 ora 1.482 1.703 2.052 2.473 more 2.473 2.771 1994 0.855 1.056 1.313 1.480 1.701 2.048 2.468 2.764 MORALES 1120 1.055 Icon 0.854 1.311 1.479 1.699 2.045 2.463 2.757 LE 0.854 1.055 1.310 2019 20 1.477 1.697 Movie 2.042 2.458 2.750 0.851 1.050 1.303 Tied 10 201 202 203 1.468 1.684 2.021 2.424 2.705 dou 0 0 100 0.849 1.047 1.299 1.462 1.676 2.009 2.404 2.678 0.848 0 1 1.045 1.296 1.458 1.671 2.000 2.391 2.661 0.847 1.044 1.294 1.456 1.667 1.994 2.381 2.648 0.846 1.043 1.292 1.453 1.664 1.990 2.374 2.639 0.846 1.042 1.291 1.452 1.662 1.987 2.369 2.632 0.845 1.042 1.290 1.451 1.660 1.984 2.365 2.626 19.65 9.937 7.115 5.876 5.201 4.783 4.500 4.297 4.297 4.144 4.025 3.930 3.930 3.852 3.788 3.733 3.687 3.646 3.611 3.580 4.318 4.221 4.141 4.073 4.015 3.965 3.922 3.884 3.850 3.552 3.820 1.492 1.059 1.318 1.316 27 28 29 30 40 50 60 70 80 90 100 3.528 3.505 3.485 3.467 3.451 3.435 3.421 3.409 3.397 3.386 3.307 3.262 3.232 3.211 3.196 3.184 3.174 3.792 3.768 3.746 3.725 2707 3.707 con 3.690 3.674 3.660 3.646 3.551 3.496 3.460 10 3.435 3.417 3.402 3.391 0842 1.036 1.282 1.440 1.645 1.960 2.327 2.576 3.091 3.291 סס w DD Tools Mobile View Share PDF to DOC