- Select a dataset from “100+ Interesting Data Sets for Statistics”
- Select one independent variable and select one dependent variable
- Independent variable: Research Grants
- Dependent variable: Academic pay
- Read the dataset as a data.table or data.frame
library("Ecdat", lib.loc="~/R/win-library/3.0")
data(University)
summary(University)
## undstudents poststudents nassets acnumbers
## Min. : 0 Min. : 26.0 Min. : 2037 Min. : 48.0
## 1st Qu.: 2678 1st Qu.: 665.2 1st Qu.: 17707 1st Qu.: 383.2
## Median : 3828 Median : 958.5 Median : 32261 Median : 558.5
## Mean : 4373 Mean :1115.1 Mean : 55043 Mean : 753.9
## 3rd Qu.: 6336 3rd Qu.:1554.2 3rd Qu.: 59737 3rd Qu.:1008.8
## Max. :10035 Max. :3975.0 Max. :406564 Max. :2030.0
## acrelnum clernum compop techn
## Min. : 11.00 Min. : 17.0 Min. : 0.00 Min. : 10.0
## 1st Qu.: 91.25 1st Qu.:193.0 1st Qu.: 6.00 1st Qu.:111.6
## Median :140.00 Median :276.5 Median : 8.50 Median :172.0
## Mean :171.88 Mean :312.9 Mean : 13.17 Mean :227.0
## 3rd Qu.:229.75 3rd Qu.:401.6 3rd Qu.: 13.75 3rd Qu.:331.1
## Max. :658.00 Max. :845.5 Max. :200.00 Max. :639.5
## stfees acpay acrelpay secrpay
## Min. : 520 Min. : 806 Min. : 0 Min. : 189.0
## 1st Qu.: 4162 1st Qu.: 8243 1st Qu.: 1110 1st Qu.: 984.2
## Median : 6065 Median :10728 Median : 2248 Median :1648.5
## Mean : 7061 Mean :14390 Mean : 2937 Mean :1934.0
## 3rd Qu.: 9248 3rd Qu.:20360 3rd Qu.: 3885 3rd Qu.:2476.2
## Max. :18800 Max. :35253 Max. :10478 Max. :8667.0
## admpay agresrk furneq landbuild
## Min. : 221 Min. : 139.0 Min. : 89 Min. : 2583
## 1st Qu.:1086 1st Qu.: 972.5 1st Qu.:1166 1st Qu.: 16855
## Median :1538 Median :1718.1 Median :1764 Median : 24744
## Mean :1872 Mean :2406.6 Mean :2419 Mean : 38635
## 3rd Qu.:2586 3rd Qu.:3396.7 3rd Qu.:3338 3rd Qu.: 41737
## Max. :4705 Max. :9147.1 Max. :9400 Max. :362000
## resgr
## Min. : 121
## 1st Qu.: 3570
## Median : 6534
## Mean : 9237
## 3rd Qu.:12150
## Max. :40746
- Describe, in detail, \(H_0\), your null hypothesis
- The null hypothesis is that there is no association/relationship between research grants and academic pay in universities in the UK.
- Describe, in detail, your (linear) model
- The linear model is testing whether there is a linear association between UK university research grants received (in pounds) and academic pay within these universities (in pounds).
- Describe the dataset you selected
- This dataset is part of a study from 1988 in the UK that looked at 62 universities and recorded a number of observations (17 in total) such as the number of undergrad and grad students, net assets, student fees, technicians, admin pay, research grants, academic pay, etc.
- The source of the dataset: Glass, J.C., D.G. McKillop and N. Hyndman (1995) “Efficiency in the provision of university teaching and research : an empirical analysis of UK universities”, Journal of Applied Econometrics, 10(1), january-march, 61-72.
- I am interested in whether the value of research grants received in an institute can predict what the pay of an academic at the institute will be.
attach(University)
lm<-lm(acpay~resgr)
- Plot the scattergram of your data
- Plot the regression line
- Plot the 95% confidence intervals of the regression line, \(b_0\) and \(b_1\)
plot(resgr,acpay,cex=1,pch=16,col="red", main="Academic pay vs. Research grants in the UK", xlab="Research Grants", ylab="Academic pay")
abline(lm$coef, lwd=2, col="green")
ci<-confint(lm,level=0.95)
abline(ci[,1],lty=2,col="green")
abline(ci[,2],lty=2,col="green")
- Print a summary of your model
summary(lm)
##
## Call:
## lm(formula = acpay ~ resgr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12055.8 -2419.1 -72.8 2137.3 12660.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.072e+03 8.364e+02 7.26 9.02e-10 ***
## resgr 9.004e-01 6.663e-02 13.51 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4460 on 60 degrees of freedom
## Multiple R-squared: 0.7527, Adjusted R-squared: 0.7486
## F-statistic: 182.6 on 1 and 60 DF, p-value: < 2.2e-16
- Interpret the results of the statistical analysis \(b_0\), \(b_1\) and \(r\)
- \(b_0\): Intercept is 6072, this is the academic pay in the absence of researh grants.
- \(b_1\): Slope of the regression line is 0.9. An increase of 1 pound in research grant funding is associated with a 0.9 pound increase in academic pay.
- \(r\): The R-squared value is 0.7527, which represents the magnitude of the correlation between academic pay and research grants.