Questions 13-22 are based on the following How much does education affect wage r
ID: 3154736 • Letter: Q
Question
Questions 13-22 are based on the following How much does education affect wage rate? Use the following data to develop an estimated regression equation that could be used to predict the WAGE for a given number of years of schooling. WAGE EDUC y x 18.7 16 11.5 12 15.04 16 25.95 14 24.03 12 20 12 53.84 16 25 12 28.85 16 16.83 13 14.8 12 43.25 16 19.23 12 14 14 8 12 57.7 21 20 12 20.83 18 22 11 68.75 14 10.5 12 9.88 13 10.96 12 8.25 13 14.86 18 23.31 13.96 13 The estimated regression equation predicts that the wage rate rises by ______ for each additional year of schooling. a $3.25 b $3.01 c $2.86 d $2.72 14 The predicted wage for a person with 16 years of schooling is, a $26.58 b $27.98 c $29.45 d $30.63 15 The sum of squared error (SSE) is, a 4739.05 b 4549.49 c 4367.51 d 4128.61 16 The sum of squares regression (SSR) is, a 1558.33 b 1498.40 c 1385.35 d 1240.77 17 The sum of squares total (SST) is, a 6369.38 b 6124.40 c 5879.43 d 5644.25 18 The observed WAGE (y) deviate from the predicted WAGE (y), on average, by, a 11.07 b 12.68 c 13.49 d 14.35 19 The fraction of variation in WAGE (y) explained by EDUC (x) is, a 0.2262 b 0.4072 c 0.4886 d 0.6840 20 The standard error of the slope coefficient is ______. a 1.161 b 0.968 c 0.858 d 0.690 21 The margin of error for a 95% confidence interval for the population slope parameter is: a 2.95 b 2.40 c 1.98 d 1.56 22 To test, at a 5% level of significance, the hypothesis H: = 0 versus H: 0, the t test statistic is|t| = ______. a 2.982 b 2.593 c 1.945 d 1.459 Questions 13-22 are based on the following How much does education affect wage rate? Use the following data to develop an estimated regression equation that could be used to predict the WAGE for a given number of years of schooling. WAGE EDUC y x 18.7 16 11.5 12 15.04 16 25.95 14 24.03 12 20 12 53.84 16 25 12 28.85 16 16.83 13 14.8 12 43.25 16 19.23 12 14 14 8 12 57.7 21 20 12 20.83 18 22 11 68.75 14 10.5 12 9.88 13 10.96 12 8.25 13 14.86 18 23.31 13.96 13 The estimated regression equation predicts that the wage rate rises by ______ for each additional year of schooling. a $3.25 b $3.01 c $2.86 d $2.72 14 The predicted wage for a person with 16 years of schooling is, a $26.58 b $27.98 c $29.45 d $30.63 15 The sum of squared error (SSE) is, a 4739.05 b 4549.49 c 4367.51 d 4128.61 16 The sum of squares regression (SSR) is, a 1558.33 b 1498.40 c 1385.35 d 1240.77 17 The sum of squares total (SST) is, a 6369.38 b 6124.40 c 5879.43 d 5644.25 18 The observed WAGE (y) deviate from the predicted WAGE (y), on average, by, a 11.07 b 12.68 c 13.49 d 14.35 19 The fraction of variation in WAGE (y) explained by EDUC (x) is, a 0.2262 b 0.4072 c 0.4886 d 0.6840 20 The standard error of the slope coefficient is ______. a 1.161 b 0.968 c 0.858 d 0.690 21 The margin of error for a 95% confidence interval for the population slope parameter is: a 2.95 b 2.40 c 1.98 d 1.56 22 To test, at a 5% level of significance, the hypothesis H: = 0 versus H: 0, the t test statistic is
|t| = ______. a 2.982 b 2.593 c 1.945 d 1.459
Explanation / Answer
The data is first copied to Excel and then imported to R and a linear model is built with x on y and the summary results are produced below which will be used to provide the answers in 13-22.
> tt <- read.csv("clipboard",header=TRUE,sep=" ")
> head(tt)
y x
1 18.70 16
2 11.50 12
3 15.04 16
4 25.95 14
5 24.03 12
6 20.00 12
> wlm <- lm(y~x,data=tt)
> summary(wlm)
Call:
lm(formula = y ~ x, data = tt)
Residuals:
Min 1Q Median 3Q Max
-20.608 -9.426 -1.605 5.611 45.320
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -18.702 16.099 -1.162 0.2568
x 3.009 1.136 2.649 0.0141 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 14.05 on 24 degrees of freedom
Multiple R-squared: 0.2262, Adjusted R-squared: 0.194
F-statistic: 7.016 on 1 and 24 DF, p-value: 0.01406
13:
14. The predicted wage for a person with 16 years of schooling is 29.4493.
> predict(wlm,newdata=data.frame(x=16))
1
29.44934
15. The sum of squared error (SSE) is, 4739.05.
> sum(residuals(wlm)^2)
[1] 4739.051
16. The sum of squares regression (SSR) is, 1385.35.
> anova(wlm)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x 1 1385.4 1385.35 7.0159 0.01406 *
Residuals 24 4739.1 197.46
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
17. The sum of squares total (SST) is, 1385.4+4739.1 = 6124.5 (or approximately
6124.4
18.
The observed WAGE (y) deviate from the predicted WAGE (y), on average, by, is 0.
19.
0.2262
20.
The standard error of the slope coefficient is 1.136 (or 1.16)
21.
The margin of error for a 95% confidence interval for the population slope parameter is:2.4.
22.
The estimated regression equation predicts that the wage rate rises by _3.01_____ for each additional year of schooling.Related Questions
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