Movie companies need to predict the gross receipts of individual movies once the movie has debuted. The following results, stored in PotterMovies, are the first weekend gross, the U.S. gross, and the worldwide gross (in $millions) of the Harry Potter movies.

a. Perform a cluster analysis using the complete linkage method on the Harry Potter movies based on the first weekend gross, the U.S. gross, and the worldwide gross (in$millions).

b. What conclusions can you reach about which Harry Potter movies are most similar?

Movie companies need to predict the gross receipts of individual movies once the movie has debuted. The following results, stored in PotterMovies, are the first weekend gross, the U.S. gross, and the worldwide gross (in millions of dollars) of the six Harry Potter movies that debuted from 2001 to 2009.

a. Construct a scatter plot with first weekend gross on the X axis and U.S. gross on the Y axis.

b. Construct a scatter plot with first weekend gross on the X axis and worldwide gross on the Y axis.

c. What can you say about the relationship between first weekend gross and U.S. gross and first weekend gross and worldwide gross?

Movie companies need to predict the gross receipts of individual movies once a movie has debuted. The data, shown below and stored in PotterMovies, are the first weekend gross, the U.S. gross, and the worldwide gross (in $millions) of the eight Harry Potter movies:$

$$\begin{array}{lrcc} \text { Title } & \begin{array}{c} \text { First } \\ \text { Weekend } \end{array} & \begin{array}{c} \text { U.S. } \\ \text { Gross } \end{array} & \begin{array}{c} \text { Worldwide } \\ \text { Gross } \end{array} \\ \hline \text { Sorcerer's Stone } & 90.295 & 317.558 & 976.458 \\ \text { Chamber of Secrets } & 88.357 & 261.988 & 878.988 \\ \text { Prisoner of Azkaban } & 93.687 & 249.539 & 795.539 \\ \text { Goblet of Fire } & 102.335 & 290.013 & 896.013 \\ \text { Order of the Phoenix } & 77.108 & 292.005 & 938.469 \\ \text { Half-Blood Prince } & 77.836 & 301.460 & 934.601 \\ \text { Deathly Hallows Part 1 } & 125.017 & 295.001 & 955.417 \\ \text { Deathly Hallows Part 2 } & 169.189 & 381.011 & 1,328.111 \end{array}$$

$

Calculate the covariance between first weekend gross and U.S. gross, first weekend gross and worldwide gross, and U.S. gross and worldwide gross.

Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions.

The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected clusters of galaxies (based on data from The Cosmic Perspective by Bennett et al., Benjamin Cummings). For the prediction interval, use a $90 \%$ confidence level with a redshift of the cluster Hydra of 0.0126.

$$\begin{array}{l|c|c|c|c|c|c} \hline \text { Redshilt } & 0.0233 & 0.0539 & 0.0718 & 0.0395 & 0.0438 & 0.0103 \\ \hline \text { Distance } & 0.32 & 0.75 & 1.00 & 0.55 & 0.61 & 0.14 \\ \hline \end{array}$$

Movie companies need to predict the gross receipts of an individual movie once the movie has debuted. The following results (stored in Potter Movies ) are the first weekend gross, the U.S. gross, and the worldwide gross (in $millions) of the eight Harry Potter movies that debuted from 2001 to 2011 :

Movie companies need to predict the gross receipts of individual movies once a movie has debuted. The data, shown below and stored in Potter Movies, are the first weekend gross, the U.S. gross, and the worldwide gross (in $millions) of the eight Harry Potter movies:$

$$\begin{array}{lrcc} \text { Title } & \begin{array}{c} \text { First } \\ \text { Weekend } \end{array} & \begin{array}{c} \text { U.S. } \\ \text { Gross } \end{array} & \begin{array}{c} \text { Worldwide } \\ \text { Gross } \end{array} \\ \hline \text { Sorcerer's Stone } & 90.295 & 317.558 & 976.458 \\ \text { Chamber of Secrets } & 88.357 & 261.988 & 878.988 \\ \text { Prisoner of Azkaban } & 93.687 & 249.539 & 795.539 \\ \text { Goblet of Fire } & 102.335 & 290.013 & 896.013 \\ \text { Order of the Phoenix } & 77.108 & 292.005 & 938.469 \\ \text { Half-Blood Prince } & 77.836 & 301.460 & 934.601 \\ \text { Deathly Hallows Part 1 } & 125.017 & 295.001 & 955.417 \\ \text { Deathly Hallows Part 2 } & 169.189 & 381.011 & 1,328.111 \end{array}$$

$ Calculate the covariance between first weekend gross and U.S. gross, first weekend gross and worldwide gross, and U.S. gross and worldwide gross.

The file Mobilespeed contains the overall download and upload speeds in mbps for nine carriers in the United States.

a. Do you think that carriers with a higher overall download speed also have a higher overall upload speed?

b. Construct a scatter plot with download speed on the X axis and upload speed on the Y axis.

c. Does the scatter plot confirm or contradict your answer in (a)?

The file Utility contains the following data about the cost of electricity (in $) during July 2018 for a random sample of 50 one-bedroom apartments in a large city.$

$$\begin{array}{rrrrrrrrrr} 96 & 171 & 202 & 178 & 147 & 102 & 153 & 197 & 127 & 82 \\ 157 & 185 & 90 & 116 & 172 & 111 & 148 & 213 & 130 & 165 \\ 141 & 149 & 206 & 175 & 123 & 128 & 144 & 168 & 109 & 167 \\ 95 & 163 & 150 & 154 & 130 & 143 & 187 & 166 & 139 & 149 \\ 108 & 119 & 183 & 151 & 114 & 135 & 191 & 137 & 129 & 158 \end{array}$$

$ Construct a cumulative percentage distribution.

The file Utility contains the following data about the cost of electricity during July of a recent year for a random sample of 50 one-bedroom apartments in a large city:

$$\begin{array}{rrrrrrrrrr} 96 & 171 & 202 & 178 & 147 & 102 & 153 & 197 & 127 & 82 \\ 157 & 185 & 90 & 116 & 172 & 111 & 148 & 213 & 130 & 165 \\ 141 & 149 & 206 & 175 & 123 & 128 & 144 & 168 & 109 & 167 \\ 95 & 163 & 150 & 154 & 130 & 143 & 187 & 166 & 139 & 149 \\ 108 & 119 & 183 & 151 & 114 & 135 & 191 & 137 & 129 & 158 \end{array}$$

Construct a histogram and a percentage polygon.

The file Utility contains the following data about the cost of electricity during July of a recent year for a random sample of 50 one-bedroom apartments in a large city:

$$\begin{array}{rrrrrrrrrr} 96 & 171 & 202 & 178 & 147 & 102 & 153 & 197 & 127 & 82 \\ 157 & 185 & 90 & 116 & 172 & 111 & 148 & 213 & 130 & 165 \\ 141 & 149 & 206 & 175 & 123 & 128 & 144 & 168 & 109 & 167 \\ 95 & 163 & 150 & 154 & 130 & 143 & 187 & 166 & 139 & 149 \\ 108 & 119 & 183 & 151 & 114 & 135 & 191 & 137 & 129 & 158 \end{array}$$

Construct a cumulative percentage polygon.

The file Mobile Speed contains the overall download and upload speeds in Mbps for eight carriers in the United States. Do you think that carriers with a higher overall download speed also have a higher overall upload speed?

Movie companies need to predict the gross receipts of individual movies once a movie has debuted. The data, shown below and stored in PotterMovies, are the first weekend gross, the U.S. gross, and the worldwide gross (in \ millions) of the eight Harry Potter movies:

$$\begin{array}{lrcc} Title & \text{First Weekend} & \text{U.S. Gross} & \text{Worldwide Gross} \\ \hline \text{Sorcerer's Stone} & 90.295 & 317.558 & 976.458 \\ \text{Chamber of Secrets} & 88.357 & 261.988 & 878.988 \\ \text{Prisoner of Azkaban} & 93.687 & 249.539 & 795.539 \\ \text{Goblet of Fire} & 102.335 & 290.013 & 896.013 \\ \text{Order of the Phoenix} & 77.108 & 292.005 & 938.469 \\ \text{Half-Blood Prince} & 77.836 & 301.460 & 934.601 \\ \text{Deathly Hallows Part 1} & 125.017 & 295.001 & 955.417 \\ \text{Deathly Hallows Part 2} & 169.189 & 381.011 & 1,328.111 \end{array}$$

a. Compute the covariance between first weekend gross and U.S. gross, first weekend gross and worldwide gross, and U.S. gross and worldwide gross.

b. Compute the coefficient of correlation between first weekend gross and U.S. gross, first weekend gross and worldwide gross, and U.S. gross and worldwide gross.

c. Which do you think is more valuable in expressing the relationship between first weekend gross, U.S. gross, and worldwide gross-the covariance or the coefficient of correlation? Explain.

d. Based on (a) and (b), what conclusions can you reach about the relationship between first weekend gross, U.S. gross, and worldwide gross?

The file Mobile Speed contains the overall download and upload speeds in Mbps for eight carriers in the United States. Construct a scatter plot with download speed on the $X$ axis and upload speed on the $Y$ axis.

The following is a stem-and-leaf display representing the gallons of gasoline purchased (with leaves in tenths of gallons) for a sample of 25 cars that use a particular service station on the New Jersey Turnpike:

$$\begin{array}{r|l} 9 & 147 \\ 10 & 02238 \\ 11 & 125566777 \\ 12 & 223489 \\ 13 & 02 \end{array}$$

How many gallons are most likely to be purchased?