Table 10.9 shows data on state educational spending per pupil (E), percentage of high school seniors taking the SAT (S), and mean reading SAT score (R).

a. Estimate the equation R = α + βE + ε.

b. Is the estimate of β positive or negative?

c. Is the estimate of β statistically significant at the 1 percent level?

d. Now estimate the equation R = α + β₁E + β₂S + ε.

e. Is the estimate of β₁ positive or negative?

f. Is the estimate of β₁ statistically significant at the 1 percent level?
g. Explain any noteworthy differences between your estimates of β in a and β1 in d.

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Table 10.9: Exercise 10.30 State E S R State E S R State E S R AK 7,877 42 443 KY 4,390 10 477 NY 8,500 69 419 AL 3,648 8 482 LA 4,012 9 473 OH 5,639 23 451 AR 3,334 7 471 MA 6,351 72 432 OK 3,742 8 479 AZ 4,231 23 452 MD 6,184 60 434 OR 5,291 63 443 CA 4,826 44 422 ME 5,894 59 431 PA 6,534 63 423 CO 4,809 29 458 MI 5,257 12 458 RI 6,989 63 429 CT 7,914 75 435 MN 5,260 15 477 SC 4,327 55 399 DC 8,210 67 407 MO 4,415 13 471 SD 3,730 6 498 DE 6,016 60 435 MS 3,322 4 472 TN 3,707 12 486 FL 5,154 47 419 MT 5,184 20 469 TX 4,238 43 415 GA 4,860 59 402 NC 4,802 57 397 UT 2,993 5 499 HI 5,008 52 406 ND 3,685 5 500 VA 5,360 59 430 IA 4,839 5 512 NE 4,381 10 487 VT 5,740 63 435 ID 3,200 17 465 5,504 66 477 WA 5,045 39 448 IL 5,062 17 462 NJ 9,159 67 423 WI 5,946 12 477 IN 5,051 55 412 NM 4,446 11 483 WV 5,046 15 448 KS 5,009 10 495 NV 4,564 23 439 WY 5,255 14 462