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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.18,0:00:01.94,Default,,0000,0000,0000,,- [Instructor] In a previous\Nvideo, we began to think about
Dialogue: 0,0:00:01.94,0:00:04.72,Default,,0000,0000,0000,,how we can use a regression\Nline and, in particular,
Dialogue: 0,0:00:04.72,0:00:08.09,Default,,0000,0000,0000,,the slope of a regression\Nline based on sample data,
Dialogue: 0,0:00:08.09,0:00:10.91,Default,,0000,0000,0000,,how we can use that in\Norder to make inference
Dialogue: 0,0:00:10.91,0:00:15.70,Default,,0000,0000,0000,,about the slope of the true\Npopulation regression line.
Dialogue: 0,0:00:15.70,0:00:17.96,Default,,0000,0000,0000,,In this video, what we're\Ngoing to think about,
Dialogue: 0,0:00:17.96,0:00:20.26,Default,,0000,0000,0000,,what are the conditions for inference
Dialogue: 0,0:00:20.26,0:00:22.61,Default,,0000,0000,0000,,when we're dealing with regression lines?
Dialogue: 0,0:00:22.61,0:00:24.90,Default,,0000,0000,0000,,And these are going to be, in some ways,
Dialogue: 0,0:00:24.90,0:00:27.28,Default,,0000,0000,0000,,similar to the conditions for inference
Dialogue: 0,0:00:27.28,0:00:30.32,Default,,0000,0000,0000,,that we thought about when we\Nwere doing hypothesis testing
Dialogue: 0,0:00:30.32,0:00:33.92,Default,,0000,0000,0000,,and confidence intervals for\Nmeans and for proportions,
Dialogue: 0,0:00:33.92,0:00:36.89,Default,,0000,0000,0000,,but there's also going to\Nbe a few new conditions.
Dialogue: 0,0:00:36.89,0:00:39.86,Default,,0000,0000,0000,,So to help us remember these conditions,
Dialogue: 0,0:00:39.86,0:00:44.86,Default,,0000,0000,0000,,you might want to think about\Nthe LINER acronym, L-I-N-E-R.
Dialogue: 0,0:00:46.95,0:00:50.50,Default,,0000,0000,0000,,And if it isn't obvious to\Nyou, this almost is linear.
Dialogue: 0,0:00:50.50,0:00:53.04,Default,,0000,0000,0000,,Liner, if it had an A, it would be linear.
Dialogue: 0,0:00:53.04,0:00:54.67,Default,,0000,0000,0000,,And this is valuable because, remember,
Dialogue: 0,0:00:54.67,0:00:57.14,Default,,0000,0000,0000,,we're thinking about linear regression.
Dialogue: 0,0:00:57.14,0:01:01.24,Default,,0000,0000,0000,,So the L right over here\Nactually does stand for linear.
Dialogue: 0,0:01:01.24,0:01:05.00,Default,,0000,0000,0000,,And here, the condition is, is\Nthat the actual relationship
Dialogue: 0,0:01:05.00,0:01:08.62,Default,,0000,0000,0000,,in the population between\Nyour x and y variables
Dialogue: 0,0:01:08.62,0:01:11.29,Default,,0000,0000,0000,,actually is a linear relationship,
Dialogue: 0,0:01:11.29,0:01:12.71,Default,,0000,0000,0000,,so actual
Dialogue: 0,0:01:13.69,0:01:14.75,Default,,0000,0000,0000,,linear
Dialogue: 0,0:01:15.67,0:01:16.85,Default,,0000,0000,0000,,relationship,
Dialogue: 0,0:01:18.36,0:01:19.31,Default,,0000,0000,0000,,relationship
Dialogue: 0,0:01:20.23,0:01:21.69,Default,,0000,0000,0000,,between,
Dialogue: 0,0:01:21.69,0:01:23.95,Default,,0000,0000,0000,,between x
Dialogue: 0,0:01:23.95,0:01:25.91,Default,,0000,0000,0000,,and y.
Dialogue: 0,0:01:25.91,0:01:28.92,Default,,0000,0000,0000,,Now, in a lot of cases, you\Nmight just have to assume
Dialogue: 0,0:01:28.92,0:01:31.27,Default,,0000,0000,0000,,that this is going to be\Nthe case when you see it on
Dialogue: 0,0:01:31.27,0:01:33.95,Default,,0000,0000,0000,,an exam, like an AP exam, for example.
Dialogue: 0,0:01:33.95,0:01:36.40,Default,,0000,0000,0000,,They might say, hey, assume\Nthis condition is met.
Dialogue: 0,0:01:36.40,0:01:37.72,Default,,0000,0000,0000,,Oftentimes, it'll say assume all
Dialogue: 0,0:01:37.72,0:01:38.60,Default,,0000,0000,0000,,of these conditions are met.
Dialogue: 0,0:01:38.60,0:01:41.10,Default,,0000,0000,0000,,They just want you to maybe\Nknow about these conditions.
Dialogue: 0,0:01:41.10,0:01:42.81,Default,,0000,0000,0000,,But this is something to think about.
Dialogue: 0,0:01:42.81,0:01:45.66,Default,,0000,0000,0000,,If the underlying\Nrelationship is nonlinear,
Dialogue: 0,0:01:45.66,0:01:47.25,Default,,0000,0000,0000,,well, then maybe some of your
Dialogue: 0,0:01:47.25,0:01:50.15,Default,,0000,0000,0000,,inferences might not be as robust.
Dialogue: 0,0:01:50.15,0:01:53.29,Default,,0000,0000,0000,,Now, the next one is\None we have seen before
Dialogue: 0,0:01:53.29,0:01:55.56,Default,,0000,0000,0000,,when we're talking about general\Nconditions for inference,
Dialogue: 0,0:01:55.56,0:01:57.53,Default,,0000,0000,0000,,and this is the independence,
Dialogue: 0,0:01:57.53,0:01:59.96,Default,,0000,0000,0000,,independence condition.
Dialogue: 0,0:01:59.96,0:02:01.98,Default,,0000,0000,0000,,And there's a couple of\Nways to think about it.
Dialogue: 0,0:02:01.98,0:02:04.07,Default,,0000,0000,0000,,Either individual observations
Dialogue: 0,0:02:04.07,0:02:05.83,Default,,0000,0000,0000,,are independent of each other.
Dialogue: 0,0:02:05.83,0:02:09.18,Default,,0000,0000,0000,,So you could be sampling with replacement.
Dialogue: 0,0:02:09.18,0:02:11.91,Default,,0000,0000,0000,,Or you could be thinking\Nabout your 10% rule,
Dialogue: 0,0:02:11.91,0:02:13.43,Default,,0000,0000,0000,,that we have done when we thought about
Dialogue: 0,0:02:13.43,0:02:18.20,Default,,0000,0000,0000,,the independence condition\Nfor proportions and for means,
Dialogue: 0,0:02:18.20,0:02:20.01,Default,,0000,0000,0000,,where we would need to feel confident
Dialogue: 0,0:02:20.01,0:02:23.71,Default,,0000,0000,0000,,that the size of our\Nsample is no more than 10%
Dialogue: 0,0:02:23.71,0:02:26.07,Default,,0000,0000,0000,,of the size of the population.
Dialogue: 0,0:02:26.07,0:02:28.14,Default,,0000,0000,0000,,Now, the next one is the normal condition,
Dialogue: 0,0:02:28.14,0:02:30.23,Default,,0000,0000,0000,,which we have talked about\Nwhen we were doing inference
Dialogue: 0,0:02:30.23,0:02:32.61,Default,,0000,0000,0000,,for proportions and for means.
Dialogue: 0,0:02:32.61,0:02:35.17,Default,,0000,0000,0000,,Although, it means something a\Nlittle bit more sophisticated
Dialogue: 0,0:02:35.17,0:02:37.58,Default,,0000,0000,0000,,when we're dealing with a regression.
Dialogue: 0,0:02:37.58,0:02:39.59,Default,,0000,0000,0000,,The normal condition, and, once again,
Dialogue: 0,0:02:39.59,0:02:42.16,Default,,0000,0000,0000,,many times people just\Nsay assume it's been met.
Dialogue: 0,0:02:42.16,0:02:43.82,Default,,0000,0000,0000,,But let me actually\Ndraw a regression line,
Dialogue: 0,0:02:43.82,0:02:44.88,Default,,0000,0000,0000,,but do it with a little perspective,
Dialogue: 0,0:02:44.88,0:02:46.67,Default,,0000,0000,0000,,and I'm gonna add a third dimension.
Dialogue: 0,0:02:46.67,0:02:48.41,Default,,0000,0000,0000,,Let's say that's the x-axis,
Dialogue: 0,0:02:48.41,0:02:50.50,Default,,0000,0000,0000,,and let's say this is the y-axis.
Dialogue: 0,0:02:50.50,0:02:54.81,Default,,0000,0000,0000,,And the true population\Nregression line looks like this.
Dialogue: 0,0:02:54.81,0:02:57.27,Default,,0000,0000,0000,,And so the normal condition tells us
Dialogue: 0,0:02:57.27,0:03:00.03,Default,,0000,0000,0000,,that, for any given x\Nin the true population,
Dialogue: 0,0:03:00.87,0:03:05.77,Default,,0000,0000,0000,,the distribution of y's that\Nyou would expect is normal,
Dialogue: 0,0:03:05.77,0:03:06.60,Default,,0000,0000,0000,,is normal.
Dialogue: 0,0:03:06.60,0:03:08.81,Default,,0000,0000,0000,,So let me see if I can\Ndraw a normal distribution
Dialogue: 0,0:03:08.81,0:03:10.91,Default,,0000,0000,0000,,for the y's,
Dialogue: 0,0:03:10.91,0:03:11.87,Default,,0000,0000,0000,,given that x.
Dialogue: 0,0:03:11.87,0:03:13.99,Default,,0000,0000,0000,,So that would be that\Nnormal distribution there.
Dialogue: 0,0:03:13.99,0:03:16.86,Default,,0000,0000,0000,,And then let's say, for\Nthis x right over here,
Dialogue: 0,0:03:16.86,0:03:21.30,Default,,0000,0000,0000,,you would expect a normal\Ndistribution as well,
Dialogue: 0,0:03:21.30,0:03:23.46,Default,,0000,0000,0000,,so just like,
Dialogue: 0,0:03:23.46,0:03:24.53,Default,,0000,0000,0000,,just like this.
Dialogue: 0,0:03:24.53,0:03:25.38,Default,,0000,0000,0000,,So if we're given x,
Dialogue: 0,0:03:25.38,0:03:27.76,Default,,0000,0000,0000,,the distribution of y's should be normal.
Dialogue: 0,0:03:27.76,0:03:29.75,Default,,0000,0000,0000,,Once again, many times you'll just be
Dialogue: 0,0:03:29.75,0:03:32.47,Default,,0000,0000,0000,,told to assume that that has\Nbeen met because it might,
Dialogue: 0,0:03:32.47,0:03:34.39,Default,,0000,0000,0000,,at least in an introductory\Nstatistics class,
Dialogue: 0,0:03:34.39,0:03:36.97,Default,,0000,0000,0000,,be a little bit hard to\Nfigure this out on your own.
Dialogue: 0,0:03:36.97,0:03:38.81,Default,,0000,0000,0000,,Now, the next condition\Nis related to that,
Dialogue: 0,0:03:38.81,0:03:42.79,Default,,0000,0000,0000,,and this is the idea of\Nhaving equal variance,
Dialogue: 0,0:03:42.79,0:03:45.09,Default,,0000,0000,0000,,equal variance.
Dialogue: 0,0:03:45.09,0:03:46.39,Default,,0000,0000,0000,,And that's just saying that each
Dialogue: 0,0:03:46.39,0:03:48.67,Default,,0000,0000,0000,,of these normal distributions should have
Dialogue: 0,0:03:48.67,0:03:51.25,Default,,0000,0000,0000,,the same spread for a given x.
Dialogue: 0,0:03:51.25,0:03:52.87,Default,,0000,0000,0000,,And so you could say equal variance,
Dialogue: 0,0:03:52.87,0:03:54.52,Default,,0000,0000,0000,,or you could even think about them having
Dialogue: 0,0:03:54.52,0:03:56.36,Default,,0000,0000,0000,,the equal standard deviation.
Dialogue: 0,0:03:56.36,0:03:59.88,Default,,0000,0000,0000,,So, for example, if, for a\Ngiven x, let's say for this x,
Dialogue: 0,0:03:59.88,0:04:02.58,Default,,0000,0000,0000,,all of sudden, you had\Na much lower variance,
Dialogue: 0,0:04:02.58,0:04:03.62,Default,,0000,0000,0000,,made it look like this,
Dialogue: 0,0:04:03.62,0:04:06.89,Default,,0000,0000,0000,,then you would no longer meet\Nyour conditions for inference.
Dialogue: 0,0:04:06.89,0:04:10.43,Default,,0000,0000,0000,,Last, but not least, and this\Nis one we've seen many times,
Dialogue: 0,0:04:10.43,0:04:12.30,Default,,0000,0000,0000,,this is the random condition.
Dialogue: 0,0:04:12.30,0:04:14.60,Default,,0000,0000,0000,,And this is that the data comes from
Dialogue: 0,0:04:14.60,0:04:17.17,Default,,0000,0000,0000,,a well-designed random sample or
Dialogue: 0,0:04:17.17,0:04:19.20,Default,,0000,0000,0000,,some type of randomized experiment.
Dialogue: 0,0:04:19.20,0:04:23.04,Default,,0000,0000,0000,,And this condition we have\Nseen in every type of condition
Dialogue: 0,0:04:23.04,0:04:25.76,Default,,0000,0000,0000,,for inference that we\Nhave looked at so far.
Dialogue: 0,0:04:25.76,0:04:27.14,Default,,0000,0000,0000,,So I'll leave you there.
Dialogue: 0,0:04:27.14,0:04:28.27,Default,,0000,0000,0000,,It's good to know.
Dialogue: 0,0:04:28.27,0:04:30.47,Default,,0000,0000,0000,,It will show up on some exams.
Dialogue: 0,0:04:30.47,0:04:32.96,Default,,0000,0000,0000,,But many times, when it\Ncomes to problem solving,
Dialogue: 0,0:04:32.96,0:04:36.13,Default,,0000,0000,0000,,in an introductory statistics\Nclass, they will tell you,
Dialogue: 0,0:04:36.13,0:04:38.72,Default,,0000,0000,0000,,hey, just assume the conditions\Nfor inference have been met.
Dialogue: 0,0:04:38.72,0:04:40.91,Default,,0000,0000,0000,,Or what are the conditions for inference?
Dialogue: 0,0:04:40.91,0:04:42.97,Default,,0000,0000,0000,,But they're not going to\Nactually make you prove,
Dialogue: 0,0:04:42.97,0:04:46.01,Default,,0000,0000,0000,,for example, the normal or\Nthe equal variance condition.
Dialogue: 0,0:04:46.01,0:04:47.04,Default,,0000,0000,0000,,That might be a bit much
Dialogue: 0,0:04:47.04,0:04:49.76,Default,,0000,0000,0000,,for an introductory statistics class.