Question

In: Statistics and Probability

Fit a multiple regression model that relates the salary to education, work experience, and time spent...

Fit a multiple regression model that relates the salary to education, work experience, and time spent at the bank so far. a - State what your model is. b - Determine whether the independent variables are significant, or not, at a level of significance of 5%. c - Which independent variable is most significant in explaining salary? Which is least significant? d - Is your overall model significant? Provide statistical proof by conducting an F-test for overall fit of the regression. State the hypothesis to be tested, the p-value for your F-statistic, and your decision. The following data is always in the same order. Salary data, in dollars (n=93): 39000,40200,42900,43800,43800,43800,43800,43800,44400,45000,45000,46200,48000,48000,48000,48000,48000,48000,48000,48000,48000,48000,49800,51000,51000,51000,51000,51000,51000,51600,52200,52200,52800,52800,52800,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,55200,55200,55800,56400,57000,57000,57000,57000,57000,60000,60000,61200,63000,63000,46200,50400,51000,51000,52200,54000,54000,54000,54000,54000,57000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,63000,66000,66000,66000,68400,69000,69000,81000 Education data, in years (n=93): 12,10,12,8,8,12,12,12,15,8,12,12,8,12,12,12,12,12,12,12,12,16,8,8,12,12,15,15,16,12,8,12,8,8,12,8,8,12,12,12,12,12,12,15,15,15,15,12,12,12,12,12,12,15,15,15,12,15,12,12,15,12,15,12,12,12,12,12,12,15,15,15,8,12,12,12,12,12,12,15,15,15,15,15,16,15,15,15,15,15,12,15,16 Previous work experience, in months (n=93): 0,44,5,6,8,0,0,5,75,52,8,52,70,6,11,11,63,144,163,228,381,214,318,96,36,59,115,165,123,18,102,127,90,190,107,173,228,26,36,38,82,169,244,24,49,51,122,97,196,133,55,90,117,51,61,241,121,79,209,87,231,12,14,180,315,29,7,38,113,18,359,36,320,24,32,49,56,252,272,25,36,56,64,108,46,72,64,84,216,42,175,132,55 Previous time spent at the bank data, in months (n=93): 1,7,30,7,6,7,10,6,2,3,19,3,20,23,12,17,22,24,12,26,1,15,25,33,15,14,1,4,12,12,29,29,11,1,11,34,33,11,33,22,29,27,1,13,27,21,33,17,32,30,9,23,25,17,11,34,30,13,21,33,15,22,3,15,2,14,21,11,3,8,11,5,21,2,17,8,33,11,19,13,32,12,33,16,3,17,16,33,16,7,10,24,33

Solutions

Expert Solution

(a) The model is:

y = 31794.798 + 1396.093*x1 + 14.840*x2 + 206.291*x3

(b) All of independent variables are significant.

(c) Education is most significant in explaining salary.

Previous work experience is least significant in explaining salary.

(d) The hypothesis being tested is:

H0: β1 = β2 = β3 = 0

H1: At least one βi ≠ 0

The test statistic is 12.84.

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

The R code is:

Salary <- c(39000,40200,42900,43800,43800,43800,43800,43800,44400,45000,45000,46200,48000,48000,48000,48000,48000,48000,48000,48000,48000,48000,49800,51000,51000,51000,51000,51000,51000,51600,52200,52200,52800,52800,52800,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,55200,55200,55800,56400,57000,57000,57000,57000,57000,60000,60000,61200,63000,63000,46200,50400,51000,51000,52200,54000,54000,54000,54000,54000,57000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,63000,66000,66000,66000,68400,69000,69000,81000)
Education <- c(12,10,12,8,8,12,12,12,15,8,12,12,8,12,12,12,12,12,12,12,12,16,8,8,12,12,15,15,16,12,8,12,8,8,12,8,8,12,12,12,12,12,12,15,15,15,15,12,12,12,12,12,12,15,15,15,12,15,12,12,15,12,15,12,12,12,12,12,12,15,15,15,8,12,12,12,12,12,12,15,15,15,15,15,16,15,15,15,15,15,12,15,16)
Previousworkexperience <- c(0,44,5,6,8,0,0,5,75,52,8,52,70,6,11,11,63,144,163,228,381,214,318,96,36,59,115,165,123,18,102,127,90,190,107,173,228,26,36,38,82,169,244,24,49,51,122,97,196,133,55,90,117,51,61,241,121,79,209,87,231,12,14,180,315,29,7,38,113,18,359,36,320,24,32,49,56,252,272,25,36,56,64,108,46,72,64,84,216,42,175,132,55)
Previoustimespent <- c(1,7,30,7,6,7,10,6,2,3,19,3,20,23,12,17,22,24,12,26,1,15,25,33,15,14,1,4,12,12,29,29,11,1,11,34,33,11,33,22,29,27,1,13,27,21,33,17,32,30,9,23,25,17,11,34,30,13,21,33,15,22,3,15,2,14,21,11,3,8,11,5,21,2,17,8,33,11,19,13,32,12,33,16,3,17,16,33,16,7,10,24,33)
mod <- lm(Salary ~ Education + Previousworkexperience + Previoustimespent)
summary(mod)

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Fit a multiple regression model that relates the salary to education, work experience, and time spent...
Fit a multiple regression model that relates the salary to education, work experience, and time spent at the bank so far. a - State what your model is. b - Determine whether the independent variables are significant, or not, at a level of significance of 5%. c - Which independent variable is most significant in explaining salary? Which is least significant? d - Is your overall model significant? Provide statistical proof by conducting an F-test for overall fit of the...
3. Fit a multiple regression model that relates the salary to education, work experience, and time spent at the bank so far.
SALARY EDUC EXPER TIME 39000 12 0 1 40200 10 44 7 42900 12 5 30 43800 8 6 7 43800 8 8 6 43800 12 0 7 43800 12 0 10 43800 12 5 6 44400 15 75 2 45000 8 52 3 45000 12 8 19 46200 12 52 3 48000 8 70 20 48000 12 6 23 48000 12 11 12 48000 12 11 17 48000 12 63 22 48000 12 144 24 48000 12 163 12...
A multiple regression model is to be constructed to model the time spent using the internet...
A multiple regression model is to be constructed to model the time spent using the internet per week among internet users. The explanatory variables are age, hours spent working per week and annual income. Data has been collected on 30 randomly selected individuals: Time using internet (minutes) Age Hours working per week Annual income ('000) 140 56 39 28 257 35 31 79 163 35 35 34 115 33 52 27 182 45 36 37 214 51 57 80 187...
Using the data, fit an appropriate regression model to determine whether time spent studying (hours) is...
Using the data, fit an appropriate regression model to determine whether time spent studying (hours) is a useful predictor of the chance of passing the exam (result, 0=fail 1=pass). Formally assess the overall fit of the model. DATA three; INPUT result hours; /* result=0 is fail; result=1 is pass */ cards; 0 0.8 0 1.6 0 1.4 1 2.3 1 1.4 1 3.2 0 0.3 1 1.7 0 1.8 1 2.7 0 0.6 0 1.1 1 2.1 1 2.8 1...
Use the least squares method to fit a simple linear model that relates the salary (dependent...
Use the least squares method to fit a simple linear model that relates the salary (dependent variable) to education (independent variable). a- What is your model? State the hypothesis that is to be tested, the decision rule, the test statistic, and your decision, using a level of significance of 5%. b – What percentage of the variation in salary has been explained by the regression? c – Provide a 95% confidence interval estimate for the true slope value. d -...
Fit a multiple regression model using MPG as the dependent variable and DISP, HP, and WT...
Fit a multiple regression model using MPG as the dependent variable and DISP, HP, and WT as the independent variables. Is the overall regression model significant? Test at the α = 0.05 level of significance. State the null hypothesis, the alternative hypothesis =, the test statistic calculated and critical values and your test conclusion. mpg disp hp wt 21 160 110 2.62 21 160 110 2.875 22.8 108 93 2.32 21.4 258 110 3.215 18.7 360 175 3.44 18.1 225...
In the​ one-period model, education can be represented as time spent by the representative consumer that...
In the​ one-period model, education can be represented as time spent by the representative consumer that is neither leisure nor time applied to producing output. What the economy gains in the future is that the representative consumer then has more time​ available, as measured in terms of effective units of labour time​ (adjusted for skill​ level, or what economists call human​ capital). That​ is, the aggregate production function can be seen as Y=zF(K, eN)​, where e is the quantity of...
Fit a multiple linear regression model of the form y=β0 + β1 x1 + β2 x2...
Fit a multiple linear regression model of the form y=β0 + β1 x1 + β2 x2 + β3 x3 + ε. Here, ε is the random error term that is assumed to be normally distributed with 0 mean and constant variance. State the estimated regression function. How are the estimates of the three regression coefficients interpreted here? Provide your output, and interpretations in a worksheet titled “Regression Output.” Obtain the residuals and prepare a box-plot of the residuals. What information...
Discuss the underlying assumptions of a simple linear regression model; multiple regression model; and polynomial regression.
Discuss the underlying assumptions of a simple linear regression model; multiple regression model; and polynomial regression.
1. Distinguish between a bivariate regression model and a multiple regression.
1. Distinguish between a bivariate regression model and a multiple regression.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT