Calculating the Effect Size, b₁

In the box below, please enter the OLS estimate of the effect of leaf thickness on weight for the data, 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 b₁ = -1.1374. Congratulations!

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

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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:

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For these data, the estimated effect of leaf thickness on weight is b₁ = -1.1374. In other words, for every 1 micron increase in thickness, the weight increases by -1.1374 grams. That is, for every 1 micron increase in thickness, the weight decreases by 1.1374 grams.

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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 effect of thickness on weight is the number in the Estimate column of the thickness 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 effect of x on y. 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 2, 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.