Pension Plan 2: A firm is interested in studying the relationship between participation in a 401k pension plan and the generosity of the plan. A random sample of n = 50 pension plans for similar firms in the same industry was collected. Data included the participation rate as a percent (prate), the 401k plan match rate (mrate)*, the total number of 401k participants (totpart), the total number of eligible employees for the 401k plan (totelg), the age of the 401k plan (age), and the total number of employees at the firm (totemp). * The 401k match rate (mrate) measures the generosity of the plan and gives the average amount the firm contributes to each worker's plan for each $1 contribution by the worker. For example, if mrate = $0.50, then a $1 contribution by the worker is matched by a 50 contribution by the firm. Build a regression model to predict participation rate from the other variables listed above. The data are contained in the worksheet named "401K" (Hint: There are more variables in the worksheet than you are instructed to use here: Be sure to construct the correct models specified in these instructions).

prate fotog 39 GL 1653 2 23 20 234 120 1 17 350 159 150 | | 34 225 519 1 9 1 1: # 13] 10 16] Botemp 079 315 275 500 29 90 | 1 31 629 13 | 23 29 252 30 237 5 1 2557 | 107 | 1 13 120 15 #1 15 598 14 3 5 24 11 20 19 mrate 021 100 76 191 100 042 25 153 100 1 10 0.53 25 02 | 18 15 10 Lil 5.5 043 9 051 100 119 100 0.41 6 1 100 0 100 L13 89 10 0 03 021 100 095 513 134 13 0 3 0% 100 087 9 000 10 091 911 53 100 020 100 1.59 [03 100 05 100 06 100 131 | 792 021 dal 100 023 11 100 23 99 052 751 0 ? 0.16 100 19 5 | 11 100 02 201 1 28% 171 3655 1 15 30 14 1 55 29 1 13 129 921 1 3110 25 32. m 1 2013 | 99 25 227 6 13 7 || 97 21 1 131 2 | 312 3543 1 458 23 121 65 1559 97 215 1 405 1125 2306 297 1024 5 129 | 109 1017 29 1-5 612 133 275 12 5 1284 103 1301 20 19 592 307 GT-LA- 20 22 7 SUMMARY OUTPUT Regression Statistics Multiple R 0.69397294 R Square 0.48159844 Adjusted R S 0.42268918 Standard Erro 11.8807176 Observations 50 ANOVA df Regression Residual Total SS MS F Significance F 5 5769.7474 1153.94948 8.17525771 1.5948E-05 44 6210.6638 141.15145 49 11980.4112 Intercept mrate totpart totelg age totemp Coefficients itandard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 86.0958238 3.66556296 23.4877493 1.5828E-26 78.7083671 93.4832805 78.7083671 93.4832805 2.17739013 2.70421146 0.80518486 0.42504287 -3.27259 7.62737021 -3.27259 7.62737021 0.01742501 0.00378954 4.59818681 3.5896E-05 0.00978769 0.02506232 0.00978769 0.02506232 -0.010635 0.00571022 -1.8624482 0.06922551 -0.0221432 0.0008732 -0.0221432 0.0008732 0.21228275 0.18963567 1.11942414 0.26903304 -0.1699028 0.59446834 -0.1699028 0.59446834 -0.0035467 0.00361512 -0.981072 0.33192113 -0.0108325 0.0037391 -0.0108325 0.0037391 Pension Plan 2: A firm is interested in studying the relationship between participation in a 401k pension plan and the generosity of the plan. A random sample of n = 50 pension plans for similar firms in the same industry was collected. Data included the participation rate as a percent (prate), the 401k plan match rate (mrate)*, the total number of 401k participants (totpart), the total number of eligible employees for the 401k plan (totelg), the age of the 401k plan (age), and the total number of employees at the firm (totemp). * The 401k match rate (mrate) measures the generosity of the plan and gives the average amount the firm contributes to each worker's plan for each $1 contribution by the worker. For example, if mrate = $0.50, then a $1 contribution by the worker is matched by a 50 contribution by the firm. Build a regression model to predict participation rate from the other variables listed above. The data are contained in the worksheet named "401K" (Hint: There are more variables in the worksheet than you are instructed to use here: Be sure to construct the correct models specified in these instructions). (a) State the model equation. PRATE = Bo + B1MRATE + B2TOTPART + B3 TOTELG + BAAGE + BETOTEMP TOTEMP = Bo + B1PRATE + B2TOTPART + B3TOTELG + B4AGE + B5PRATE O PRATE = B1 MRATE + B2 TOTPART + B3TOTELG + B4AGE + B5TOTEMP MRATE = Bo + B1PRATE + B2 TOTPART + B3TOTELG + BAAGE + B5TOTEMP MRATE = B_PRATE + B2TOTPART + B3TOTELG + BAAGE + BETOTEMP (b) Provide the sample-based model coefficient for match rate. (Round your answer to three decimal places.) % Interpret the model coefficient for match rate (MRATE) by mentally inserting the ABSOLUTE VALUE of the coefficient in the blanks below. % for every additional dollar in match rate. According to the sample data, participation rate increases on average by According to the sample data, match rate decreases on average by $ According to the sample data, match rate increases on average by $ According to the sample data, participation rate decreases on average by for every additional percentage point in participation rate. for every additional percentage point in participation rate. % for every additional dollar in match rate. (c) Test the significance of match rate in determining participation rate after accounting for the effects of all the other explanatory variables. Use a 10% significance level. State the hypotheses to be tested. O Ho: B1 = 0 Ha: B1 0 O Ho: B4 = 0 Ha: B4 0 0 O Ho: Bo = 0 Ha: Bo #0 Ho: B2 = 0 Ha: B2 0 0 O Ho: B3 = 0 Ha: B3 70 Interpret the hypotheses you specified above. Ho: There is no linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. Ha: There is a linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. Ho: There is a linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. Ha: There is no linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. Ho: None of the explanatory variables are important in explaining/predicting participation rate. Ha: At least one explanatory variable is important in explaining/predicting participation rate. Ho: All of the explanatory variables are important in explaining/predicting participation rate. Ha: None of the explanatory variables are important in explaining/predicting participation rate. State the decision rule. Reject Ho if p value 0.10. Do not reject Ho if p value 0.05. Do not reject Ho if p value 0.10. Do not reject Ho if p value 0.05. Do not reject Ho if p value