Week 4 Homework
In a scatterdiagram, the _______ variable is plotted on the horizontal axis and the
_______ variable is plotted on the vertical axis.
Explanatory, response
The linear correlation coefficient is always between _______ and _______, inclusive.
-1, 1
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The closer r is to +1, the _______ the evidence is of _______ association between
the two variables.
Stronger, positive
T/F: If r is close to0, then little or no evidence exists of a relation between the two
quantitative variables.
False.
A value of r close to zero does not imply norelation, just no linear relation.
What is the linear correlation coefficient?
A measure of the strength and direction of the linear relationship between two
variables.
Why should correlations should always be reported with scatter diagrams?
The scatter diagram is needed to see if the correlation coefficient is being affected by
the presence of outliers.
What does it mean if r=0?
No linear relationship exists between the variables.
What does it mean to say that two variables are positivelyassociated?
There is a linear relationship between thevariables, and whenever the value of one
variableincreases, the value of the other variable increases.
What does it mean to say that two variables are negativelyassociated?
There is a linear relationship between thevariables, and whenever the value of one
variableincreases, the value of the other variable decreases.
Explain what each point on theleast-squares regression line represents.
Each point on theleast-squares regression line represents the predictedy-value at
the corresponding value of x.
How do you calculate residual?
Observed y minus predicted y.
What is the least-squares regression line?
The line of best fit; it minimizes the sum of the squared residuals.
Which of the following is true about the least squares regression line, y = b₁x + b₀?
The least-squares regression line always contains the point (⁻x,⁻y)
The predicted value of y, ^y, is an estimate of the mean value of the response
variable for that particular value of the explanatory variable.
, The least-squares regression line minimizes the sum of squared residuals.
The sign of the linear correlation coefficient, r, and the sign of the slope of the
least-squares regression line, b₁, are the same.
What is the slope-intercept form?
y = mx + b
m is the slope and b is the y-intercept.
A student at a junior college conducted a survey of 20 randomly selectedfull-time
students to determine the relation between the number of hours of video game
playing eachweek, x, andgrade-point average, y. She found that a linear relation
exists between the two variables. Theleast-squares regression line that describes
this relation is y = -0.0572x + 2.9205
a) Predict thegrade-point average of a student who plays video games 8 hours per
week.
b) Interpret the slope.
c) Ifappropriate, interpret they-intercept.
a) y = (-0.0572*8) + 2.9205 = 2.46
b) For each additional hour that a student spends playing video games in aweek,
thegrade-point average will decrease by 0.0572 points, on average.
c) Thegrade-point average of a student who does not play video games is 2.9205.
(x=0)
Is there a relation between the age difference betweenhusband/wives and the
percent of a country that isliterate? Researchers found theleast-squares regression
between age difference(husband age minus wifeage), y, and literacy rate(percent
of the population that isliterate), x, is y = −0.0498x + 6.8.
The model applied for 17≤x≤100.
a) Interpret the slope.
b) Does it make sense to interpret they-intercept? Explain.
c) Predict the age difference betweenhusband/wife in a country where the literacy
rate is 30 percent.
d) Would it make sense to use this model to predict the age difference between
husband/wife in a country where the literacy rate is 12%?
e) The literacy rate in a country is 97% and the age difference between husbands
and wives is 1.5 years. Is this age difference above or below the average age
difference among all countries whose literacy rate is 97%
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