Statistics and probability
- Constructing a scatter plot
- Constructing scatter plots
- Making appropriate scatter plots
- Example of direction in scatterplots
- Scatter plot: smokers
- Bivariate relationship linearity, strength and direction
- Positive and negative linear associations from scatter plots
- Describing trends in scatter plots
- Positive and negative associations in scatterplots
- Outliers in scatter plots
- Clusters in scatter plots
- Describing scatterplots (form, direction, strength, outliers)
- Scatterplots and correlation review
In a negative linear association, as one variable goes up, the other variable goes down at a constant rate. In this case, the percent of adults who smoke drops 0.5% each time the year goes up. In the right graph, the points go down by about 0.5% each year. There should be no points far away from the main trend. Created by Sal Khan.
Want to join the conversation?
- At 00:9, sal says linear association what does that mean?(7 votes)
- This is hard is there an easier way to do this.??(6 votes)
- Stick with it! You'll get it. What may help is to brush up on basic shapes of functions (ie: linear= straight line, logarithmic, exponential, polynomial, etc). These are taught in Pre-Calc and Calc classes already. A suggestion to Khan Academy might be to do a quick video and practice review section at the beginning of this section to review what linear/ non-linear functions look like in graph (non-scatter) form...and since I suggested it, I'll even do the video if you want me to, just show me the tools and code to upload the wmv. :-)(18 votes)
- At1:02, what does Sal mean by an outlier in the graph?(3 votes)
- Who here is from the year 10239786413?(7 votes)
- I'm from India.
I also see some people smoking for a living. Really they should stop.
anyways, nice video! :)(7 votes)
- Wait so how would you just identify a linear or not linear if 2 look the same like graph 1 and graph 2.(3 votes)
- Graph 1 and graph 2 are both linear. You cannot identify them with linear association.
Instead, in the question, it said that percent drops by 0.5 point each year.
You have to compare two different points and figure it out.(5 votes)
- what is a linear line(2 votes)
- That sounds redundant, a linear function creates a line. The exception to the function is an x=# which is also a line, but not a function.(2 votes)
The percent of adults who smoke recorded every few years since 1967 suggests a negative linear association with no outliers. On average, the percent drops by 0.5 points each year. Which of the following plots suits the above description? So let's see, this looks like a negative linear association. As the years go by, you have a smaller percentage of smokers. This one does too. As years go by, you have the number of smokers go down and down. This one down here also looks like that, although it's not as smooth. If you were to fit a line here, it looks like you have a few outliers. Well, this is a positive correlation. So we can definitely rule out Graph 4. Now, the other thing that they told us is that there are no outliers, suggests a negative linear association with no outliers. If you were to try to fit a line to Graph 3, you could fit a line pretty reasonably. That would go someplace like that. But it would have this outlier right over here. It looks like it's 12 or 13 years after 1967. So that would be 1980. It looks like an outlier there. But they said it didn't have any outliers. So we would rule out Graph 3. And so we have to pick between Graph 1 and Graph 2. So the other hint they give us or piece of data they give us is that the percent drops by 0.5% each year. So here's what's happening. In 1967, it looks like we're at about 55%. And then 10 years go by. We are roughly at around 45, a little under 45%. So we dropped 10% in 10 years. That seems to be how much this is dropping, roughly 10% in 10 years. Another 10 years go by. We go from 45, a little more than 10% in 10 years. And so that would mean that we're dropping, on average, more than one percentage point per year. That seems more than what's going on here. Now, let's look over here. Over here, we're starting, it looks like, at around 42%. And then after 10 years, it looks like we're at 37%. So it looks like we've dropped about 5% in 10 years, which is consistent with this. If you drop 5% in 10 years, that means you drop half a percent per year. So we'll go with Graph 2.