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How to find the 95% confidence interval for the slope of regression line in R?
The slope of the regression line is a very important part of regression analysis, by finding the slope we get an estimate of the value by which the dependent variable is expected to increase or decrease. But the confidence interval provides the range of the slope values that we expect 95% of the times when the sample size is same. To find the 95% confidence for the slope of regression line we can use confint function with regression model object.
Example
Consider the below data frame −
set.seed(1) x <-rnorm(20) y <-rnorm(20,2.5) df <-data.frame(x,y) df
Output
x y 1 -0.62645381 3.4189774 2 0.18364332 3.2821363 3 -0.83562861 2.5745650 4 1.59528080 0.5106483 5 0.32950777 3.1198257 6 -0.82046838 2.4438713 7 0.48742905 2.3442045 8 0.73832471 1.0292476 9 0.57578135 2.0218499 10 -0.30538839 2.9179416 11 1.51178117 3.8586796 12 0.38984324 2.3972123 13 -0.62124058 2.8876716 14 -2.21469989 2.4461950 15 1.12493092 1.1229404 16 -0.04493361 2.0850054 17 -0.01619026 2.1057100 18 0.94383621 2.4406866 19 0.82122120 3.6000254 20 0.59390132 3.2631757
Creating regression model to predict y from x −
Example
RegressionModel <-lm(y~x,data=df) summary(RegressionModel)
Output
Call: lm(formula = y ~ x, data = df) Residuals: Min 1Q Median 3Q Max -1.69133 -0.43739 -0.07132 0.68033 1.63937 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.5331 0.1998 12.677 2.08e-10 *** x -0.2075 0.2195 -0.946 0.357 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.8738 on 18 degrees of freedom Multiple R-squared: 0.04732, Adjusted R-squared: -0.00561 F-statistic: 0.894 on 1 and 18 DF, p-value: 0.3569
Finding the 95% confidence interval for the slope of the regression line −
Example
confint(RegressionModel,'x',level=0.95) 2.5 % 97.5 % x -0.6687129 0.2536177 Lets’ have a look at another example: BloodPressure <-c(165,170,190,195,220) Weight <-c(50,75,64,60,62) data <-data.frame(BloodPressure,Weight) data
Output
BloodPressure Weight 1 165 50 2 170 75 3 190 64 4 195 60 5 220 62
Example
RegM <-lm(BloodPressure~Weight,data=data) summary(RegM)
Output
Call: lm(formula = BloodPressure ~ Weight, data = data) Residuals: 1 2 3 4 5 -21.783 -19.277 1.820 7.219 32.020 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 181.79551 88.73672 2.049 0.133 Weight 0.09975 1.41495 0.070 0.948 Residual standard error: 25.34 on 3 degrees of freedom Multiple R-squared: 0.001654, Adjusted R-squared: -0.3311 F-statistic: 0.00497 on 1 and 3 DF, p-value: 0.9482
Example
confint(RegM,'Weight',level=0.95) 2.5 % 97.5 % Weight -4.403255 4.602756
Output
2.5 % 97.5 % Weight -4.403255 4.602756
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