Deck 7: Linear Regression

Question 1

If the point in the upper right corner of this scatterplot is removed from the data set, then What will happen to the slope of the line of best fit (b) and to the correlation (r)?

A)b will increase, and r will decrease.
B)b will decrease, and r will increase.
C)both will decrease.
D)both will increase.
E)both will remain the same.

Answer 1

b will decrease, and r will increase.

Question 2

Create a model to predict postal rates from the year.

Answer 2

Question 3

Interpret the slope of your model in context.

Answer 3

Slope of the model is 0.0101518.The model predicts that for every additional year the first class postal rate will increase by $0.01, on average.

Question 4

A small independent organic food store offers a variety of specialty coffees.To determine Whether price has an impact on sales, the managers kept track of how many pounds of each Variety of coffee were sold last month.
$$\begin{array} { | l | l | l | } \hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \\\hline & \$ 3.99 & 75 \\\hline & \$ 5.99 & 60 \\\hline & \$ 7.00 & 65 \\\hline & \$ 12.00 & 45 \\\hline & \$ 4.50 & 80 \\\hline & \$ 7.50 & 70 \\\hline & \$ 15.00 & 25 \\\hline & \$ 10.00 & 35 \\\hline & \$ 12.50 & 40 \\\hline & \$ 8.99 & 50\\\hline & \\\hline \text { Mean } &\$8.75&54.50 \\\hline \begin{array} { l } \text { Standard } \\\text { Deviation }\end{array} & \$ 3.63 & 18.33 \\\hline \text { Correlation } & - \mathbf { 0 . 9 2 7 } \\\hline\end{array}$$

Based on the data and summary statistics, the intercept of the estimated regression line that Relates the response variable (monthly sales) to the predictor variable (price per pound) is

A)95.459.
B).858.
C)-4.684.
D)-.858.
E)-8.999.

Question 5

Explain the meaning of } R ² in the context of this problem.

Question 6

Interpret the intercept of your model in context.

Question 7

Residuals are …

A)the difference between observed responses and values predicted by the model.
B)data collected from individuals that is not consistent with the rest of the group.
C)none of these
D)possible models not explored by the researcher.
E)variation in the data that is explained by the model.

Question 8

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:




-Make a scatterplot and describe the association between the size of the diamond (carat) and the cost (in US dollars).

Question 9

Explain the meaning of R ² in the context of this problem.

Question 10

What is the correlation between cost and size?

Question 11

An article in the Journal of Statistics Education reported the price of diamonds of different sizes in Singapore dollars (SGD). The following table contains a data set that is consistent with this data, adjusted to US dollars in 2004:




-Create a model to predict diamond costs from the size of the diamond.

Question 12

A small independent organic food store offers a variety of specialty coffees.To determine Whether price has an impact on sales, the managers kept track of how many pounds of each Variety of coffee were sold last month.
$$\begin{array} { | l | l | l | } \hline & \text { PRICE PER POUND } & \text { POUNDS SOLD } \\\hline & \$ 3.99 & 75 \\\hline & \$ 5.99 & 60 \\\hline & \$ 7.00 & 65 \\\hline & \$ 12.00 & 45 \\\hline & \$ 4.50 & 80 \\\hline & \$ 7.50 & 70 \\\hline & \$ 15.00 & 25 \\\hline & \$ 10.00 & 35 \\\hline & \$ 12.50 & 40 \\\hline & \$ 8.99 & 50\\\hline & \\\hline \text { Mean } &\$8.75&54.50 \\\hline \begin{array} { l } \text { Standard } \\\text { Deviation }\end{array} & \$ 3.63 & 18.33 \\\hline \text { Correlation } & - \mathbf { 0 . 9 2 7 } \\\hline\end{array}$$
Based on the data and summary statistics shown below, the slope of the estimated regression
Line that relates the response variable (monthly sales) to the predictor variable (price per
Pound) is

A)95.459.
B).858.
C)-4.681.
D)-.858.
E)-8.999.

Question 13

Do you think a linear model is appropriate here? Explain.

Question 14

What is the correlation between year and postal rate?

Question 15

Question 16

A small independent organic food store offers a variety of specialty coffees.To determine Whether price has an impact on sales, the managers kept track of how many pounds of each Variety of coffee were sold last month.
$$\begin{array} { | l | l | l | } \hline \text { Mean } & \$ 8.75 & 54.50 \\\hline \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \$ 3.63 & 18.33 \\\hline \text { Correlation } & - \mathbf { 0 . 9 2 7 } & \\\hline\end{array}$$
Based on the summary statistics shown below, what percent of the variability in the number of pounds of coffee sold per week can be explained by price?

A)95.47%
B)100%
C)85.9%
D)55.6%
E)4.68%

Question 17

Interpret the slope of your model in context.

Question 18

Make a scatterplot and describe the association between the year and the

Question 19

Interpret the intercept of your model in context.

Question 20

Do you think a linear model is appropriate here? Explain.

Question 21

The correlation coefficient between high school grade point average (GPA) and college GPA is 0.560.For a student with a high school GPA that is 2.5 standard deviations above the Mean, we would expect that student to have a college GPA that is ______ the mean.

A)0.56 SD above
B)1.94 SD above
C)2.5 SD above
D)equal to
E)1.4 SD above

Question 22

If the point in the upper left corner of the scatterplot is removed, what will happen to the Correlation (r) and the slope of the line of best fit (b)?

A)r will decrease and b will increase.
B)r will increase and b will decrease.
C)Both will decrease.
D)Both will increase.
E)They will not change.

Question 23

Question 24

An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on the circumference of a plate by using the diameter in inches. Their model is ${\hat{\text { cheerios }}}$ $= 0.56 + 5.11$ (diameter).
The slope of this model is best interpreted in context as...

A) For every $5.11$ inches of diameter, the circumference is about 1 cheerio bigger.
B) For every 1 inch of diameter, the circumference holds about $0.56$ more cheerios.
C) It takes $5.11$ cheerios to fill a plate's circumference.
D) For every 1 inch of diameter, the circumference holds about $5.11$ more cheerios.
E) A mistake, because $\pi$ is about $3.14$ and that should be the slope.

Question 25

Question 26

Question 27

Question 28

Question 29

A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found $R ^ { 2 } = 0.311$ . Which of these is true?
I. High school GPA accounts for $31.1 \%$ of college GPA.
II. $31.1 \%$ of college GPAs can be correctly predicted with this model.
III. $31.1 \%$ of the variance in college GPA can be accounted for by the model

A) I only
B) II only
C) III only
D) I and II
E) none of these

Question 30

Suppose the correlation, r, between two variables x and y is -0.44.What percentage of the
Variability in y cannot be explained by x?

A)19%
B)44%
C)81%
D)88%
E)12%