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Multiple Linear Regression in R | R Tutorial 5.3 | MarinStatsLectures - YouTube
Channel: MarinStatsLectures-R Programming & Statistics
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hi I'm Mike Marin and in this video
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we'll introduce multiple linear
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regression multiple linear regression is
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useful for modeling the relationship
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between a numeric outcome dependent or Y
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variable and multiple explanatory
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independent or X variables we will be
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working with the lung capacity data that
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was introduced earlier in this series of
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videos I've already gone ahead and
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imported the data into R and attached it
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our outcome variable will be lung
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capacity to fit our linear model we will
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be using the LM commit you can access
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the help menu by typing help and the
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name of the command in brackets or by
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typing the command name directly into
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the help search window
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we will be working with scripts in our
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you can see I have one prepared here
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having worked through my series of
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videos you should be a bit more
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comfortable using our at this point to
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learn more about writing or saving
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scripts in our see my video in series
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one on writing scripts in our first
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let's fit a linear regression model
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using age and height as our explanatory
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or X variables and let's save this in an
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object called model one will submit this
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command here and now let's ask for a
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summary of this model here we can see
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the r-squared of zero point eight four
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three approximately 84% of variation in
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lung capacity can be explained by our
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model that is can be explained by age
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and height here we can see the F
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statistic and p-value for an overall
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test of significance of our model this
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tests the null hypothesis that all of
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the model coefficients are 0 in our
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example here a test specifically that
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the slope for age and height are zero
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here we can see the residual standard
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error this gives us an idea of how far
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observed lung capacities or Y values are
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from the predicted or fitted lung
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capacity the Y hats this gives us an
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idea of the typical sized residual or
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error the intercept of negative eleven
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point seven four seven is the estimated
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mean Y value when all X's are zero this
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would be the estimated mean lung
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capacity for someone of H and height
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zero you'll notice that this doesn't
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have a very meaningful interpretation to
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give the intercept a better
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interpretation we can Center age and
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height this is a topic we'll discuss in
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following videos we can see that the
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slope for age is zero point 1 to 6 this
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is the effect of age on lung capacity
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adjusting or controlling for height we
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associate an increase of 1 year in age
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with an increase of 0.1 to 6 in lung
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capacity adjusting or controlling for
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the height we can also see the
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hypothesis test that the slope equals 0
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here
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the slope for height is 0.278 this is
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the estimated effect of height on lung
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capacity adjusting for age we can see
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the test for the hypothesis that the
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slope for height is zero here now let's
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go ahead and calculate Pearson's
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correlation between age and height we
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can see that age and height are very
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highly correlated the collinearity
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between age and height means that we
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should not directly interpret the slopes
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say the slope of age as the effective
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age on lung capacity adjusting for
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height this high correlation between age
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and height suggests that these two
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effects are somewhat founded together
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dealing with collinearity is a topic
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we'll discuss in later videos and
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finally as we've seen in earlier videos
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we can create a confidence interval for
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the model coefficients using the comp
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int command let's go ahead and take a
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look at a confidence interval for our
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model coefficients we have an estimated
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slope for age of zero point 1 to 6 where
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95% confident the true slope is between
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0.09 and 0.16 let's go ahead and fit a
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linear model using all of our X
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variables we'll submit this command here
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and now we can ask for a summary of our
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model we can check the model assumptions
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by examining plots of the residuals or
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errors to do so we can use the plot
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model command taking a look at these
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plots here we can see the relationship
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between age height and lung capacity is
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approximately linear the variation looks
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constant lung capacity given age and
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height is approximately normal to learn
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more about producing and examining these
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residual plots you can see my earlier
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video on examining model assumptions in
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linear regression in the next video in
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this series we'll talk more about linear
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regression and specifically we will
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focus our discussion on the inclusion of
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categorical variables or factors in a
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linear model thanks for watching this
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video and make sure to check out
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other instructional videos
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