nasal length nasal width 609 2
nasal length | nasal width |
609 | 241 |
629 | 222 |
620 | 233 |
564 | 207 |
645 | 247 |
493 | 189 |
606 | 226 |
660 | 240 |
630 | 215 |
672 | 231 |
778 | 263 |
616 | 220 |
727 | 271 |
810 | 284 |
778 | 279 |
823 | 272 |
755 | 268 |
710 | 278 |
701 | 238 |
803 | 255 |
855 | 308 |
838 | 281 |
830 | 288 |
864 | 306 |
635 | 236 |
565 | 204 |
562 | 216 |
580 | 225 |
596 | 220 |
597 | 219 |
636 | 201 |
559 | 213 |
615 | 228 |
740 | 234 |
677 | 237 |
675 | 217 |
629 | 211 |
692 | 238 |
710 | 221 |
730 | 281 |
763 | 292 |
686 | 251 |
717 | 231 |
737 | 275 |
816 | 275 |
In the kangaroo noses tab in the data file, We have data on thenasal length and width of grey kangaroos in mm. Use this data tocomplete the following exercises.
a) Run a regression and report your findings with nasal lengthas the dependent variable and nasal width as the independentvariable, i.e. length = b0 + b1 × width
b) Interpret the estimate for b1.
c) Test the hypothesis that the ?1 coefficient is equal to1.
d) Construct a 95% confidence interval for the b0coefficient.
Answer:
nasal length | nasal width | (X-Mx)^2 | (Y-My)^2 | (X-Mx)(Y-My) | Y’ | (Y-Y’)^2 | |
609 | 241 | 6146.56 | 9.957531 | 247.3956 | 221.6067 | 376.0983 | |
629 | 222 | 3410.56 | 490.8686 | 1293.884 | 227.359 | 28.71881 | |
620 | 233 | 4542.76 | 124.4464 | 751.8844 | 224.7705 | 67.72497 | |
564 | 207 | 15227.56 | 1380.535 | 4584.996 | 208.6642 | 2.769526 | |
645 | 247 | 1797.76 | 8.090864 | -120.604 | 231.9608 | 226.1778 | |
493 | 189 | 37791.36 | 3042.135 | 10722.24 | 188.2437 | 0.571973 | |
606 | 226 | 6625.96 | 329.6242 | 1477.862 | 220.7439 | 27.62649 | |
660 | 240 | 750.76 | 17.26864 | 113.8622 | 236.275 | 13.8758 | |
630 | 215 | 3294.76 | 850.0464 | 1673.529 | 227.6466 | 159.9366 | |
672 | 231 | 237.16 | 173.0686 | 202.5956 | 239.7263 | 76.14875 | |
778 | 263 | 8208.36 | 355.1131 | 1707.307 | 270.2132 | 52.03078 | |
616 | 220 | 5097.96 | 583.4909 | 1724.707 | 223.62 | 13.10464 | |
727 | 271 | 1568.16 | 720.6242 | 1063.04 | 255.545 | 238.8569 | |
810 | 284 | 15030.76 | 1587.58 | 4884.929 | 279.4168 | 21.00543 | |
778 | 279 | 8208.36 | 1214.135 | 3156.907 | 270.2132 | 77.20722 | |
823 | 272 | 18387.36 | 775.3131 | 3775.707 | 283.1558 | 124.4517 | |
755 | 268 | 4569.76 | 568.5575 | 1611.884 | 263.5982 | 19.37627 | |
710 | 278 | 510.76 | 1145.446 | 764.8844 | 250.6556 | 747.7165 | |
701 | 238 | 184.96 | 37.89086 | -83.7156 | 248.0671 | 101.3462 | |
803 | 255 | 13363.36 | 117.602 | 1253.618 | 277.4035 | 501.9188 | |
855 | 308 | 28089.76 | 4076.113 | 10700.33 | 292.3594 | 244.6287 | |
838 | 281 | 22680.36 | 1357.513 | 5548.773 | 287.47 | 41.86062 | |
830 | 288 | 20334.76 | 1922.335 | 6252.218 | 285.1691 | 8.014112 | |
864 | 306 | 31187.56 | 3824.735 | 10921.73 | 294.9479 | 122.1489 | |
635 | 236 | 2745.76 | 66.51309 | 427.3511 | 229.0847 | 47.82182 | |
565 | 204 | 14981.76 | 1612.469 | 4915.04 | 208.9518 | 24.52034 | |
562 | 216 | 15725.16 | 792.7353 | 3530.707 | 208.089 | 62.58448 | |
580 | 225 | 11534.76 | 366.9353 | 2057.307 | 213.266 | 137.6871 | |
596 | 220 | 8353.96 | 583.4909 | 2207.818 | 217.8678 | 4.54634 | |
597 | 219 | 8172.16 | 632.802 | 2274.062 | 218.1554 | 0.713353 | |
636 | 201 | 2641.96 | 1862.402 | 2218.196 | 229.3723 | 804.9863 | |
559 | 213 | 16486.56 | 970.6686 | 4000.373 | 207.2261 | 33.3376 | |
615 | 228 | 5241.76 | 261.002 | 1169.662 | 223.3324 | 21.7863 | |
740 | 234 | 2766.76 | 103.1353 | -534.182 | 259.284 | 639.2789 | |
677 | 237 | 108.16 | 51.20198 | 74.41778 | 241.1644 | 17.34212 | |
675 | 217 | 153.76 | 737.4242 | 336.7289 | 240.5892 | 556.4486 | |
629 | 211 | 3410.56 | 1099.291 | 1936.284 | 227.359 | 267.6167 | |
692 | 238 | 21.16 | 37.89086 | -28.3156 | 245.4786 | 55.92905 | |
710 | 221 | 510.76 | 536.1798 | -523.316 | 250.6556 | 879.4543 | |
730 | 281 | 1814.76 | 1357.513 | 1569.573 | 256.4078 | 604.7742 | |
763 | 292 | 5715.36 | 2289.091 | 3617.04 | 265.8991 | 681.2596 | |
686 | 251 | 1.96 | 46.84642 | -9.58222 | 243.7529 | 52.52048 | |
717 | 231 | 876.16 | 173.0686 | -389.404 | 252.6689 | 469.5404 | |
737 | 275 | 2460.16 | 951.3798 | 1529.884 | 258.4211 | 274.859 | |
816 | 275 | 16537.96 | 951.3798 | 3966.596 | 281.1425 | 37.73038 | |
Mean | 687.4 | 244.1556 | |||||
Sum | 30933 | 10987 | 377508.8 | 40195.91 | 108576.2 | 10987 | 8968.053 |
a) Y’=b0+b1*Width
b) To interpret, for every additonal unit of input output valueincreases by 0.287612 units.
c)
To test hypothesis:
and
Df= n-2= 43
The test statistic:
P-value= 0.000
The test statistic is significant and rejects H0 at coefficientvalue equal to 1. THere is insufficient evidence to support theclaim that the coeffciient value is equal to 1.
d) 95% Confidence interval for b0:
t critical: