# 7.3: An Example of Simple Regression

- Page ID
- 7237

The following example uses a measure of peoples’ political ideology to predict their perceptions of the risks posed by global climate change. OLS regression can be done using the `lm`

function in `R`

. For this example, we are again using the class data set.

`ols1 <- `**lm**(ds$glbcc_risk~ds$ideol)
**summary**(ols1)

```
##
## Call:
## lm(formula = ds$glbcc_risk ~ ds$ideol)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.726 -1.633 0.274 1.459 6.506
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.81866 0.14189 76.25 <0.0000000000000002 ***
## ds$ideol -1.04635 0.02856 -36.63 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.479 on 2511 degrees of freedom
## (34 observations deleted due to missingness)
## Multiple R-squared: 0.3483, Adjusted R-squared: 0.348
## F-statistic: 1342 on 1 and 2511 DF, p-value: < 0.00000000000000022
```

The output in R provides quite a lot of information about the relationship between the measures of ideology and perceived risks of climate change. It provides an overview of the distribution of the residuals; the estimated coefficients for ^αα^ and ^ββ^; the results of hypothesis tests; and overall measures of model fit" – all of which we will discuss in detail in later chapters. For now, note that the estimated BB for ideology is negative, which indicates that as the value for ideology * increases*—in our data this means more conservative—the perceived risk of climate change

*. Specifically, for each one-unit increase in the ideology scale, perceived climate change risk decreases by -1.0463463.*

*decreases*We can also examine the distribution of the residuals, using a histogram and a density curve. This is shown in Figure \(\PageIndex{4}\) and Figure \(\PageIndex{5}\). Note that we will discuss residual diagnostics in detail in future chapters.

**data.frame**(ols1$residuals) %>%
**ggplot**(**aes**(ols1$residuals)) +
**geom_histogram**(bins = 16)

**data.frame**(ols1$residuals) %>%
**ggplot**(**aes**(ols1$residuals)) +
**geom_density**(adjust = 1.5)

For purposes of this Chapter, be sure that you can run the basic bivariate OLS regression model in `R`

. If you can – congratulations! If not, try again. And again. And again…

- Actually, we assume only that the
**means**of the errors drawn from repeated samples of observations will be normally distributed – but we will deal with that wrinkle later on.↩