Chapter #10 - 10/30/24

Question 1

explain the difference between deterministic and statistical relationship

Question 2

Describe a linear pattern in a scatterplot.

Question 3

Describe how a correlation relates to the strength and direction of a linear relationship.

Question 4

Describe a linear pattern using a regression line

Question 5

Do you think each of the following pairs of variables would have a positive
correlation, a negative correlation, or no correlation?

b. Calories eaten per day and IQ

Answer 5

no correlation (not a clear relationship)

Question 5

Do you think each of the following pairs of variables would have a positive
correlation, a negative correlation, or no correlation?

a. Calories eaten per day and weight

Answer 5

positive correlation

Question 5

define “correlation” :

Answer 5

measures the strength of a certain type of relationship (e.g., linear relationship) between two measurement variables.

Question 6

define “deterministic” :

Answer 6

if we know the value of one variable, we can determine the value of the other exactly. e.g. relationship between volume and weight of water.

Question 6

define “regression” :

Answer 6

gives a numerical method for trying to predict one measurement variable from another.

Question 7

define “statistical” :

Answer 7

natural variability exists in both measurements. Useful for describing what happens to a population or aggregate.

Question 8

when is a relationship statistically significant ?

Answer 8

if the chances of observing the relationship in the sample when nothing is going on in the population are less than 5% (small).

Question 9

what are two warnings about statistical significance ?

Answer 9

• even a minor relationship will achieve “statistical significance” if the sample is very large.
• A very strong relationship won’t necessarily achieve “statistical significance” if the sample is very small.

Question 10

what is a scatterplot ?

Question 11

when creating a scatterplot, if there is an explanatory variable, where do we plot it ?

Answer 11

on the horizontal axis (x axis)

Question 12

How sensitive to changes in water temperature are coral reefs. Scientists examined data on mean sea surface temperatures (in degrees Celcius) and mean coral growth (in centimeters per year) over a several-year period at locations in the Gulf of Mexico.

Sea surface temperature and Growth

what is the response variable ?

Answer 12

coral reef growth

Question 13

what letter represets correlation ?

Answer 13

r

Question 14

what does r represent ?

Answer 14

indicator of how closely the values fall to a straight line.

Question 15

what does correlation measure ?

Answer 15

linear relationships only (that is, it measures how close the individual points in a scatterplot are to a straight line)

Question 16

what are some features of correlations ?

Answer 16

1. Correlation of +1 indicates a perfect linear relationship between the two variables; as one increases, so does the other. All individuals fall on the same straight line (a deterministic linear relationship).
2. Correlation of –1 also indicates a perfect linear relationship between the two variables; however, as one increases, the other decreases.
3. Correlation of zero could indicate no linear relationship between the two variables, or that the best straight line through the data on a scatterplot is exactly horizontal.
4. A positive correlation indicates that the variables increase together.
5. A negative correlation indicates that as one variable increases, the other decreases.
6. Correlations are unaffected if the units of measurement are changed. For example, the correlation between weight and height remains the same regardless of whether height is expressed in inches, feet or millimeters (as long as it isn’t rounded off).

Question 16

if 0.5 less than or equal|r| less than 0.8 what does this mean ?

Answer 16

moderate

Question 17

if |r| less than or equal to 0.5, what does this this mean ?

Answer 17

weak

Question 18

if |r| greater than or equal to 0.8, what does this mean ?

Answer 18

strong

Question 19

Choose the option that best answers the following question.
If the correlation (r) between two variables is close to 0, you can conclude that a scatterplot would show :
a) a strong straight-line pattern
b) a cloud of points with no visible pattern.
c) no straight-line pattern, but there may be a strong pattern of another form.

Answer 19

c) no straight-line pattern, but there may be a strong pattern of another form.

Question 20

when specifying linear relationships with regression? what is the goal ?

Answer 20

find a straight line that comes as close to possible to the point in a scatterplot

Question 21

what is the procedure to find the line is called ?

Answer 21

regression

Question 22

what is the resulting line called ?

Answer 22

regression line

Question 23

what is the formula that describes the line is called ?

Answer 23

the regression equation

Question 24

what does the most common procedure used give ?

Answer 24

the least squares regression line

Question 25

what formula do we use to find the equation of the line ?

Answer 25

y = a + b(x)

Question 26

in the formula : y = a + b(x)

what does “a” represent ?

Answer 26

the intercept (where the line crosses the vertical axis where x=0)

Question 27

at the intercept, where the line crosses the vertical axis, what does x = ?

Answer 27

x = 0

Question 28

in the formula : y = a + b(x)

what does “b” represent ?

Answer 28

slope (how much of an increase/decrease there is in y when x increases by one unit

Question 29

what is “extrapolation” ?

Answer 29

the action of estimating or concluding something by assuming that existing trends will continue or a current method will remain applicable.

Question 32

FILL IN THE BLANK

____________ is NOT a good idea to use a regression equation to predict values far outside the range where the original data fell.

Answer 32

extrapolation

Question 34

TRUE OR FALSE

in extrapolation, there is no guarantee that the realtionship will continue beyonf the range for which we have data ?

Answer 34

TRUE

Question 35

when do we use the extrapolation equation ?

Answer 35

use the equation only for minor extrapolation beyond the range of the original data

Question 36

what is easy to be misled by inappropriate interprestatins and uses of correlation and regression ?

Answer 36

extrapolation

Question 37

The regression line for body fat index (bfi) as a function of tricep thickness (in mm) is given below.

bfi = 14.59 + (0.74 × triceps thickness)

What is the average amount by which bfi changes when tricep thickness increases by 1 mm?
a) 1.48
b) 14.59
c) 14.59 + 0.74
d) 0.74

Answer 37

d) 0.74

Question 38

The regression line for body fat index (bfi) as a function of tricep thickness (in mm) is given below.

bfi = 14.59 + (0.74 × triceps thickness)

Predict the bfi for individuals with tricep thickness of 35 mm.

a) 15.33
b) 49.59
c) 40.49
d) 25.9

Answer 38

c) 40.49