Statistics Chapter 4: Scatterplots and Correlation

1. Statistical relationships are ____, not ____. AKA? 2. Response variable - 3. Explanatory variable - 4. example. How does drinking beer affect the level of alcohol in our blood? The legal limit for driving in all states is 0.08%. Student volunteers at the Ohio State University drank different numbers of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content. What is the explanatory variable and what is the Response variable? 5. The goal in many studies is to show..

1. Overall tendencies ; ironclad rules ; correlation is not causation 2. Measure an outcome of a study 3. May explain or influence change in a response variable 4. Explanatory = # of beers ; Response = Blood alcohol % 5. changes in explanatory variables actually causes change in a response variable.

Cautions to keep in mind when you use r: 1. Correlation requires that both variables be ____, that that is makes sense to do the arithmetic indicated by the formula for r. 2. Correlation measure the strength of only the .... ; Correlation does not describe _____ between variables no matter how strong they are. 3. Like the mean and standard deviation, the correlation is not ___. r is... 4. Correlation is not ... even when the relationship is between the variables is linear. You should give the ____ along with the correlation.

1. Quantitative 2. linear relationship between 2 variables ; curved relationships. 3. resistant ; strongly affected by a. few outlying observations. 4. a complete summary of 2-variable data ; means and standard deviations of both x and y

1. The most useful graph for displaying the relationship between two quantitative variables is a?

1. Scatterplot (state, plan, solve)

Facts About Correlation 1. R is positive when.. 2. R is negative when.. 3. Correlation makes no distinction between.. 4. When r uses that standardized values of observations.. 5. Positive R indicates .... Negative R indicates.... 6. The correlation is always a number between ? 7. Values near 0 indicate? 8. the strength of the linear relationship increases as.. 9. Values close to -1 or 1 indicate..

1. There is a positive association between the variables. Ex. Height and weight. 2. the association between x and y is negative. 3. explanatory and response variables. Doesn't not matter which variable you call x and y. 4. r does not change when we change the units of measurement for x and y. R itself has no unit of measurement. 5. positive association between the variables ; negative association. 6. -1 and 1 7. a very weak linear relationship. 8. r moves away from 0 towards either -1 or 1 9. that the points in a scatterplot lie close to a straight line.

1. An overall patter that follows a straight line from lower left to upper right? 2. it is always wise to ask? 3. A linear relationship is strong if the points.. 4. it is weak if they are? 5. Can we use our eyes to make this decision? 6. What measure do we use for this analysis?

1. a linear relationship 2. what other variables lurking in the background might contribute to the relationship displayed in a scatterplot. 3. lie close to a straight line 4. widely scattered about a line. 5. Hell naw nig 6. Correlation

Interpreting scatterplots 1. In any graph, look for the ____ and for ____ from the pattern. 2. How do you describe the overall patter of a scatterplot? 3. What is an important deviation?

1. overall pattern ; striking deviations 2. direction, form, and strength of the relationship. 3. An outlier

1. Two variables are ____ when above average values of not tend accompany above average values of the other. Same term is applied to below average values that accompany one another. 2. Two variables are ____ when above average values of one tend to accompany below average values of the other, or vice versa.

1. positively associated ex. The taller the athletes are, the more rebounds they earn per game on average. 2. negatively associated ex. the more students that take the mcat, the lower the mean MCAT score is.

1. Correlation measures.. 2. symbol? 3. formula?

1. the direction and strength of the linear relationship between 2 quantitative variables. 2. r 3. pic

Chapter 4 Summary 1. To study relationships between variables, we must measure the variables on? 2. If we think that a variable (x) may explain or even cause change in another variable (y), We call x a _____ and y a ____. 3. A ____ displays the relationship between 2 quantitative variables measure on the same individuals. Mark values of one variable on the ____ and values of the other variable on the ____. Plot each individual's data as a? Always plot the ____, if there is one, on the x axis of a scatterplot. 4. Plot points with different colours or symbols to see.. 5. In examining a scatterplot, look for an overall pattern showing ___, ____, & ____ of the relationship and then for ____ or other deviations from this pattern.

1. the same group of individuals 2. explanatory variable ; response variable 3. Scatterplot ; horizontal axis (x axis) ; vertical axis (y axis) ; point on the graph ; explanatory variable 4. the effect of a categorical variable in a scatterplot. 5. strength, direction, form ; outliers

1. A scatter plot show the relationship between two quantitative variables measured on.. 2. Always plot the explanatory variable.. 3. therefor we refer to the explanatory variable as? and the response variable as? 4. if there is no distinction between the types of variables?

1. the same individuals 2. on the x-axis 3. y ; x 4. either variable can go on the x axis.

Adding Categorical Variables to Scatterplots 1. What do you do when adding a categorical variable to a scatterplot?

1. use a different plot color or symbol for each category.

Chapter 4 summary cont'd 6. Direction: If a relationship as a clear direction, we speak of either positive association ( .... ) or negative association ( .... ). 7. Form: Linear relationships, where the points show a ____, are an important form of relationship between two variables. Curved relationships and ____ are other forms to watch for. 8. Strength: The strength of a relationship is determined by ... 9. The correlation measures the ___ and ____ of the linear association between 2 quantitive variables x and y. Although you can calculate a correlation for any scatterplot, r measures only.. 10. Correlation indicates the direction of a linear relationship by its sign: r > 0 for a ___ and r < 0 for a ___. Correlation always satisfies -1 < r < 1 and indicates strength of a relationship by how close it is to? Perfect correlation, ___, occurs only when the points on a scatterplot lie... 11. Correlation ignores the distinction between? The value of r is not affected by changes in? Correlation is not ___, so outliers can greatly change the value of r.

6. high values of the two variables tend to occur together ; high values of one variable tend to occur with low values of the other variable. 7. straight-line pattern ; clusters 8. how close the points in the scatterplot lie to a simple form such as a line. 9. direction & strength ; straight-line relationships 10. positive association ; negative association ; -1 or 1 ; +/-1 ; exactly on a straight line. 11. explanatory variables & response variables ; units of measurement ; resistant.