Pension Plan 1: A firm is interested in studying the factors that influence employee participation in a 401(k) pension plan. Build a regression model to forecast participation rate (as a percent) (prate) from total 401k participants (totpart), total eligible for 401k plan (totelg), and total number of firm employees (totemp). (Hint: There are more variables in the worksheet than you are instructed to use here). The data are contained in the worksheet named "401K". (a) State the model equation. MRATE = 1PRATE + 2TOTPART + 83TOTELG + B4AGE + B5TOTEMP O TOTEMP = Bo + 1PRATE + 32TOTPART + B3TOTELG + B4AGE + BSPRATE PRATE = B,TOTPART + $2TOTELG + B3TOTEMP MRATE = Bo + 1PRATE + 2TOTPART + B3TOTELG + B4AGE + B5TOTEMP O PRATE = Bo + 1TOTPART + 82TOTELG + B3TOTEMP (b) Find a point estimate of the average participation rate for any number of plans with 262 total 401k participants, 262 total eligible for 401k plan, and 315 total number of firm employees. (Round your answer to two decimal places.) 90.70 * % Correctly interpret your answer immediately above by mentally inserting that value into the blanks below. Our best interval estimate for the participation rate for one particular pension plan that fit this profile is _ %. Our best interval estimate for the average participation rate of all pension plans that fit this profile is _% O Our best single number estimate for the participation rate for one particular pension plan that fit this profile is O Our best single number estimate for the average participation rate of all pension plans that fit this profile is % X (c) Find a 95% interval estimate of the average participation rate for any number of plans with 262 total 401k participants, 262 total eligible for 401k plan, and 315 total number of firm employees. (Round your answers to two decimal places.) Correctly interpret your answer immediately above by mentally inserting that values into the blanks below. Based on a sample of 50 pension plans, we are 95% confident that the true average participation rate for pension plans in the sample that fit this profile is between % Based on a sample of 50 pension plans, we are 0.05 confident that the true average participation rate for pension plans in the sample that fit this profile is between % and Based on a sample of 50 pension plans, we are 95% confident that the true average participation rate for all pension plans that fit this profile is between % and O Based on a sample of 50 pension plans, we are 0.05 confident that the true average participation rate for all pension plans that fit this profile is between % and % . (d) Find a point estimate of the participation rate for a single plan with 262 total 401k participants, 262 total eligible for 401k plan, and 315 total number of firm employees. (Round your answer to two decimal places.) % Correctly interpret your answer immediately above by mentally inserting that value into the blanks below.A B C D E F G H K L M N mrate O P prate totpart Q R totelg age totemp sole Itotemp 26.1 0.21 1653 6322 8 8709 0 9.072112 100 1.42 262 262 6 315 OUT A W NY 1 5.752573 97.6 0.91 166 170 10 275 5.616771 100 0.42 257 257 7 500 0 6.214608 82.5 0.53 591 716 28 933 1 6.838405 100 1.82 92 92 7 143 1 4.962845 100 0.53 399 399 31 628 10 00 1 6.44254 92.5 0.34 210 227 13 823 0 6.712956 10 100 0.22 234 234 21 279 1 5.631212 96.8 0.6 120 124 10 141 1 4.94876 12 83 0.5 156 188 5 252 0 5.529429 13 100 1.11 187 187 20 237 1 5.46806 14 65.5 0.43 350 534 5 681 1 6.523562 15 84.9 0.51 1519 1790 10 2557 0 7.84659 16 100 0. 19 150 150 7 187 1 5.231109 17 100 0.41 160 160 7 188 5.236442 18 100 0.84 3448 3448 13 4120 0 8.323608 19 77.6 0.46 225 290 15 341 0 5.831882 20 100 0.45 519 519 15 598 0 6.393591 21 100 1.13 176 176 8 273 5.609472 22 66.9 0.48 79 118 224 1 5.411646 23 100 0.39 270 270 415 0 6.028278 24 70.3 0.21 201 286 361 0 5.888878 25 100 0.95 381 381 23 422 0 6.045005 401K COST, HW9 RD5 COMPREPS PISTONS | ThirdWorld Software Cost TRAFFIC6 SP5 ... +X (c) Find a 95% interval estimate of the average participation rate for any number of plans with 262 total 401k p= nts, 262 total eligible for 401k plan, and 315 total number of firm employees. (Round your answers to two decimal places.) Press F11 to exit full screen Correctly interpret your answer immediately above by mentally inserting that values into the blanks below. Based on a sample of 50 pension plans, we are 95% confident that the true average participation rate for pension plans in the sample that fit this profile is between % and Based on a sample of 50 pension plans, we are 0.05 confident that the true average participation rate for pension plans in the sample that fit this profile is between % and % . Based on a sample of 50 pension plans, we are 95% confident that the true average participation rate for all pension plans that fit this profile is between %% and 0 . O Based on a sample of 50 pension plans, we are 0.05 confident that the true average participation rate for all pension plans that fit this profile is between % and %. (d) Find a point estimate of the participation rate for a single plan with 262 total 401k participants, 262 total eligible for 401k plan, and 315 total number of firm employees. (Round your answer to two decimal places.) % Correctly interpret your answer immediately above by mentally inserting that value into the blanks below. Our best interval number estimate for the average participation rate of all pension plans that fit this profile is % . O Our best single number estimate for the participation rate for one particular pension plan that fits this profile is % Our best single number estimate for the average participation rate of all pension plans that fit this profile is %. Our best interval number estimate for the participation rate for one particular pension plan that fits this profile is (e) Find a 95% interval estimate for the participation rate for a single plan with 262 total 401k participants, 262 total eligible for 401k plan, and 315 total number of firm employees. (Round your answers to two decimal places.) Correctly interpret your answer immediately above by mentally inserting that values into the blanks below. Based on a sample of 50 pension plans, we are 95% confident that the true participation rate for one particular pension plan that fits this profile is between % and Based on a sample of 50 pension plans, we are 0.05 confident that the true participation rate for one particular pension plan that fits this profile is between % and Based on a sample of 50 pension plans, we are 0.05 confident that the true average participation rate for all pension plans that fit this profile is between % and Based on a sample of 50 pension plans, we are 95% confident that the true average participation rate for all pension plans that fit this profile is between % and % (f) State why the prediction interval is wider than the confidence interval. The standard error for the prediction of a single observation is | always larger than the standard error for the prediction of a conditional mean.26 51.3 0.34 284 554 9 797 1 6.680855 21 61.3 0.36 171 279 15 2102 1 7.650645 28 88.3 0.96 3858 4371 28 4371 0 8.382747 29 100 0.87 143 143 143 1 4.962845 OO 30 82.9 4.2 107 129 131 1 4.875197 31 77.8 0.08 70 990 1042 0 6.948897 100 0.91 179 179 312 1 5.743003 33 90.1 0.44 2803 3110 6 3543 0 8.172729 34 85.3 0.62 93 109 13 158 0 5.062595 35 100 0.28 425 125 458 0 6.126869 36 100 0.59 2027 2027 7 2442 0 7.800573 37 75.6 0.3 438 579 11 1721 0 7.450661 38 100 0.56 584 584 685 1 6.529419 39 100 0.65 1284 1284 1559 0 7.3518 40 100 1.31 109 109 37 297 1 5.693732 41 78.2 0.21 1017 1301 2125 0 7.661527 42 77.4 0.41 209 270 381 1 5.9428 43 100 0.23 145 145 405 0 6.003887 44 77 0.41 612 795 12 1125 0 7.025538 15 100 2.03 133 133 35 206 1 5.327876 46 98.9 0.52 275 278 42 297 0 5.693732 47 75.3 0.39 192 255 6 1024 0 6.931472 48 77.2 0. 16 464 601 636 0 6.455199 49 100 0.99 542 542 622 0 6.43294 50 88.5 0.1 3107 3510 6428 0 8.768418 51 100 0.02 732 732 2284 0 7.733684 401K COST, HW9 RD5 COMPREPS PISTONS ThirdWorld Software Cost TRAFFIC6 SP5 ... (+)