Calculating the y-intercept, b₀

In the box below, please enter the OLS estimate of the y-intercept, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

Your guess:

You got the correct answer of b₀ = 8.0952. Congratulations!

Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.

Show Formula

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Here is the formula you can use to calculate the OLS estimate of the effect.

In this formula, there are a few symbols to know:

Show Solution

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For these data, the estimated leaf weight when thickness is zero is b₀ = 8.0952 grams.

Show the R Code

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Copy and paste the following code into your R script window, then run it from there.

In the R output, the estimated y-intercept is the number in the Estimate column of the (Intercept) row. If you would like better precision for that value, or if you would like to have only that value, run the following code in addition to that above:

Here, the number outputted is the estimated y-intercept. How did you get the number? The summary table (also known as a regression table) is just a table. Thus, the first line saves the table as the variable modSummary the last line looks inside that variable, selects the regression table, and then selects the row 1, column 1 value.

The alternative method uses the coefficients functions to get the coefficients directly from the model. The estimated y-intercept is value [1], and the estimated slope is value [2]. The difference between the two methods is that the second method only accesses the coefficients. The first method can access the coefficients, standard errors, test statistics, etc.