3: Exploratory Data Analysis: Relationships between variables

Question 1

scatterplot

Answer 1

shows relationship b/w two quant. variables measured on the same individuals.

values of one variable appear on horiz axis and values of other appear on vert axis. each individual in the data appears as the point in the plot fixed by the values of both variables for that individual

Question 2

for scatterplot, the explanatory variable always goes on which axis?

Answer 2

explanatory variable (if there is one) is on X axis
response variable is on Y

Question 3

two variables are __________ when above average values of one tend to accompany above average values of the other and below average values also tend to occur together

Answer 3

two variables are POSITIVELY ASSOCIATED when above average values of one tend to accompany above average values of the other and below average values also tend to occur together

Question 4

two variables are ______________ when above-average values of one tend to accompany below average values of the other and vice versa

Answer 4

two variables are NEGATIVELY ASSOCIATED when above-average values of one tend to accompany below average values of the other and vice versa

Question 5

strength of a scatterplot relationship is shown by…

Answer 5

how closely the points follow a clear form (e.g. line)

Question 6

transformation of data

Answer 6

we replace the original values by the transformed values and then use the transformed values for our analysis

Question 7

correlation

Answer 7

measures the direction and strength of the linear relationship b/w 2 quant variables. r.

if we have data for x and y for n individuals… The means and std deviation of the two variables are xbar and Sx for the x-values and ybar and Ys for the y values, the correlation is:

PASTE FORMULA HERE

Question 8

correlation indicates the direction of a linear relationship by its sign. r > 0 for ____ association and r < 0 for ________ association.

Answer 8

correlation indicates the direction of a linear relationship by its sign. r > 0 for POSITIVE association and r < 0 for NEGATIVE association.

Question 9

correlation is/is not a resistant measure.

Answer 9

correlation is not a resistant measure.

Question 10

normal distributions

Answer 10

1. density curve is always on or above the X axis
2. density curve has exactly 1.0 total area beneath it
3. normal distrib describes overall pattern of a distribution
4. area under the curve and above (or below) any value is the relative frequency of all observations that fall in that range

Question 11

center and spread of density curves

1. mode
2. median
3. mean

Answer 11

1. mode = peak point
2. median = point at which half the total area is on each side
3. mean - point at which curve would balance if solid

Question 12

In Normal Curve….
approx ____% of observations fall within 1 std. dev of mean
approx ____% of observations fall within 2 std. dev of mean
approx ____% of observations fall within 3 std. dev of mean

Answer 12

1. 68
2. 95
3. 99.7

Question 13

Crosstab measures ____ and ____ variables. Rows are responsible for ___ variable and columns are ____ variable.

Answer 13

Crosstab measures CAT and CAT variables. Rows are responsible for RESPONSE variable and columns are EXPLANATORY variable.

Question 14

In a scatterplot, the response variable = ___ axis and the explanatory variable = ___ axis

Answer 14

In a scatterplot, the response variable = Y axis

and the explanatory variable = X axis

Question 15

correlation

Answer 15

standardized measure of the direction and strength of the linear relationship b/w 2 quant variables

ranges from -1.0 to 1.0

b/c r uses the standardized values of the observations, the correlation doesn’t change when we change units of measurement

correlation ignores distinction b/w response and explanatory variable

correlation r is strongly affected by a few outlying observations