The number of vehicles sold in the United States (in millions) for each year is shown in the table below, along with the proportion of those vehicles that were made by General Motors.

$$\begin{array}{lcc} \text { Year } & \text { Cars Sold (millions) } & \text { Percent GM } \\ \hline 1950 & 6.0 & 50.2 \\ 1955 & 7.8 & 50.4 \\ 1960 & 7.3 & 44.0 \\ 1965 & 10.3 & 49.9 \\ 1970 & 10.1 & 39.5 \\ 1975 & 10.8 & 43.1 \\ 1980 & 11.5 & 44.0 \end{array}$$

$$\begin{array}{ccc} \text { Year } & \text { Cars Sold (millions) } & \text { Percent GM } \\ \hline 1985 & 15.4 & 40.1 \\ 1990 & 13.5 & 36.0 \\ 1995 & 15.5 & 31.7 \\ 2000 & 17.4 & 28.6 \\ 2005 & 16.9 & 26.9 \\ 2010 & 11.6 & 19.1 \\ 2015 & 17.5 & 17.6 \end{array}$$

To find the answers to the following questions, use a statistical software programme. Is the number of cars sold directly or indirectly related to GM’s percentage of the market? Draw a scatter diagram to show your conclusion.

The hotel and restaurant operations of a suburban hotel are the source of its income. The proprietors are curious about the connection between the number of rooms that are regularly occupied and the restaurant's daily earnings. The restaurant revenue and number of rooms occupied for a sample of 25 days (Monday through Thursday) from last year are displayed below.

$$\begin{array}{rcc} \text { Day } & \text { Revenue } & \text { Occupied } \\ 1 & \$ 1,452 & 23 \\ 2 & 1,361 & 47 \\ 3 & 1,426 & 21 \\ 4 & 1,470 & 39 \\ 5 & 1,456 & 37 \\ 6 & 1,430 & 29 \\ 7 & 1,354 & 23 \\ 8 & 1,442 & 44 \\ 9 & 1,394 & 45 \\ 10 & 1,459 & 16 \\ 11 & 1,399 & 30 \\ 12 & 1,458 & 42 \\ 13 & 1,537 & 54 \end{array}$$

$$\begin{array}{ccc} \text { Day } & \text { Revenue } & \text { Occupied } \\ \hline 14 & \$ 1,425 & 27 \\ 15 & 1,445 & 34 \\ 16 & 1,439 & 15 \\ 17 & 1,348 & 19 \\ 18 & 1,450 & 38 \\ 19 & 1,431 & 44 \\ 20 & 1,446 & 47 \\ 21 & 1,485 & 43 \\ 22 & 1,405 & 38 \\ 23 & 1,461 & 51 \\ 24 & 1,490 & 61 \\ 25 & 1,426 & 39 \end{array}$$

To find the answers to the following questions, use a statistical software programme. Does the revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.

The proportion of variation in the dependent variable that is explained by the variation in the independent variable is measured by the ________ .

There are locations of Bi-lo Appliance Super-Store in a number of significant New England cities. Prior to a sale that began on Saturday and ended on Sunday, the general sales manager ran a digital camera commercial on a few local TV stations. She gathered data on the Saturday-Sunday digital camera sales at numerous stores and compared it to the quantity of times the commercial appeared on nearby TV stations. The goal is to determine if there is any connection between the frequency of the advertisement and sales of digital cameras. The combinations are:

$$\begin{array}{|lcc|} \hline \begin{array}{l} \text { Location of } \\ \text { TV Station } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Airings } \end{array} & \begin{array}{c} \text { Saturday-Sunday Sales } \\ \text{ (\$ thousands) } \end{array} \\ \hline \text { Providence } & 4 & 15 \\ \text { Springfield } & 2 & 8 \\ \text { New Haven } & 5 & 21 \\ \text { Boston } & 6 & 24 \\ \text { Hartford } & 3 & 17 \\ \hline \end{array}$$

Using this, interpret these statistical measures.

Study of recall of TV commercials. Do TV shows with violence and sex impair memory for commercials? To respond to this question, Iowa State researchers conducted a designed experiment in which $324$ adults were randomly assigned to one of three viewer groups of $108$ participants each (Journal of Applied Psychology, June $2002$). One group watched a TV program with a violent content code ($\text V$) rating, the second group viewed a show with a sex content code ($\text S$) rating, and the last group watched a neutral TV program with neither a $\text V$ nor an $\text S$ rating. Nine commercials were embedded into each TV show. After viewing the program, each participant was scored on his or her recall of the brand names in the commercial messages, with scores ranging from $0$ (no brands recalled) to $9$ (all brands recalled). The data (simulated from information provided in the article) are saved in the accompanying file. The researchers compared the mean recall scores of the three viewing groups with an analysis of variance for a completely randomized design.

a. Determine the experimental units in the study.

Do TV shows with violence and sex impair memory for commercials? To respond this question, Iowa State researchers conducted a designed experiment in which 324 adults were randomly assigned to one of three viewer groups of 108 participants each (Journal of Applied Psychology, June 2002). One group watched a TV program with a violent content code (V) rating, the second group viewed a show with a sex content code (S) rating, and the last group watched a neutral TV program with neither a $\mathrm{V}$ nor an $\mathrm{S}$ rating. Nine commercials were embedded into each TV show. After viewing the program, each participant was scored on his or her recall of the brand names in the commercial messages, with scores ranging from 0 (no brands recalled) to 9 (all brands recalled). The data (simulated from information provided in the article) are saved in the accompanying file. The researchers compared the mean recall scores of the three viewing groups with an analysis of variance for a completely randomized design.

Analysis of Variance

Model Summary

b. Determine the dependent (response) variable in the analysis.

Do TV shows with violence and sex impair memory for commercials? To respond this question, Iowa State researchers conducted a designed experiment in which 324 adults were randomly assigned to one of three viewer groups of 108 participants each (Journal of Applied Psychology, June 2002). One group watched a TV program with a violent content code (V) rating, the second group viewed a show with a sex content code (S) rating, and the last group watched a neutral TV program with neither a $\mathrm{V}$ nor an $\mathrm{S}$ rating. Nine commercials were embedded into each TV show. After viewing the program, each participant was scored on his or her recall of the brand names in the commercial messages, with scores ranging from 0 (no brands recalled) to 9 (all brands recalled). The data (simulated from information provided in the article) are saved in the accompanying file. The researchers compared the mean recall scores of the three viewing groups with an analysis of variance for a completely randomized design.

Analysis of Variance

Model Summary

g. Check that the ANOVA assumptions are reasonably satisfied.

There are locations of Bi-lo Appliance Super-Store in a number of significant New England cities. Prior to a sale that began on Saturday and ended on Sunday, the general sales manager ran a digital camera commercial on a few local TV stations. She gathered data on the Saturday-Sunday digital camera sales at numerous stores and compared it to the quantity of times the commercial appeared on nearby TV stations. The goal is to determine if there is any connection between the frequency of the advertisement and sales of digital cameras. The combinations are:

$$\begin{array}{|lcc|} \hline \begin{array}{l} \text { Location of } \\ \text { TV Station } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Airings } \end{array} & \begin{array}{c} \text { Saturday-Sunday Sales } \\ \text{ (\$ thousands) } \end{array} \\ \hline \text { Providence } & 4 & 15 \\ \text { Springfield } & 2 & 8 \\ \text { New Haven } & 5 & 21 \\ \text { Boston } & 6 & 24 \\ \text { Hartford } & 3 & 17 \\ \hline \end{array}$$

. Using this, determine the correlation coefficient.

There are locations of Bi-lo Appliance Super-Store in a number of significant New England cities. Prior to a sale that began on Saturday and ended on Sunday, the general sales manager ran a digital camera commercial on a few local TV stations. She gathered data on the Saturday-Sunday digital camera sales at numerous stores and compared it to the quantity of times the commercial appeared on nearby TV stations. The goal is to determine if there is any connection between the frequency of the advertisement and sales of digital cameras. The combinations are:

$$\begin{array}{|lcc|} \hline \begin{array}{l} \text { Location of } \\ \text { TV Station } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Airings } \end{array} & \begin{array}{c} \text { Saturday-Sunday Sales } \\ \text{ (\$ thousands) } \end{array} \\ \hline \text { Providence } & 4 & 15 \\ \text { Springfield } & 2 & 8 \\ \text { New Haven } & 5 & 21 \\ \text { Boston } & 6 & 24 \\ \text { Hartford } & 3 & 17 \\ \hline \end{array}$$

Using this, draw a scatter diagram.

There are locations of Bi-lo Appliance Super-Store in a number of significant New England cities. Prior to a sale that began on Saturday and ended on Sunday, the general sales manager ran a digital camera commercial on a few local TV stations. She gathered data on the Saturday-Sunday digital camera sales at numerous stores and compared it to the quantity of times the commercial appeared on nearby TV stations. The goal is to determine if there is any connection between the frequency of the advertisement and sales of digital cameras. The combinations are:

$$\begin{array}{|lcc|} \hline \begin{array}{l} \text { Location of } \\ \text { TV Station } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Airings } \end{array} & \begin{array}{c} \text { Saturday-Sunday Sales } \\ \text{ (\$ thousands) } \end{array} \\ \hline \text { Providence } & 4 & 15 \\ \text { Springfield } & 2 & 8 \\ \text { New Haven } & 5 & 21 \\ \text { Boston } & 6 & 24 \\ \text { Hartford } & 3 & 17 \\ \hline \end{array}$$

What is the dependent variable?

Engine size and emissions were shown to be correlated by 0.47 in a study of 12 cars conducted by the Environmental Protection Agency. Can we say that there is a positive correlation between these variables at the .01 level of significance? What does p-value mean? Interpret.

According to a sociologist, a student's college success (as indicated by their GPA) is correlated with the family's income. The correlation coefficient for a sample of 20 students is 0.40. Can we infer that there is a positive correlation between the variables at the .01 significance level?

Using a random sample of 25 flights, a local commuter airline discovered a 0.94 link between the number of passengers and the total weight of bags stored in the luggage compartment. Can we say that there is a positive relationship between the two variables at the .05 level of significance?

The Masters, one of the most prestigious golf competitions on the PGA Tour, is held each April in Augusta, Georgia. There were 55 winners of prizes in 2016. Danny Willett, the victor in 2016, received a reward worth $1,800,000. With$880,000 in prize money, Jordan Spieth and Lee Westwood tied for second place. Although two amateur players placed "in the money," they were unable to accept their winnings. The data does not contain them. The information is succinctly summarised below. Finishing position, score, and award are the three associated variables for each player (in dollars). We wish to investigate the connection between performance and reward.

$$\begin{array}{|llcl|} \hline \text { Position } & \text { Player } & \text { Score } & \text { Prize } \\ \hline 1 & \text { Danny Willett } & 283 & \$ 1,800,000 \\ 2(\text { tied) } & \text { Jordan Spieth } & 286 & \$ 880,000 \\ 2(\text { tied) } & \text { Lee Westwood } & 286 & \$ 880,000 \\ 4(\text { tied) } & \text { Paul Casey } & 287 & \$ 413,333 \\ 4(\text { tied) } & \text { J.B. Holmes } & 287 & \$ 413,333 \\ 4(\text { tied) } & \text { Dustin Johnson } & 287 & \$ 413,333 \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ 52(t i e d) & \text { Keegan Bradley } & 301 & \$ 24,900 \\ 52(t i e d) & \text { Larry Mize } & 301 & \$ 24,900 \\ 54 & \text { Hunter Mahan } & 302 & \$ 24,000 \\ 55 \text { (tied) } & \text { Kevin Na } & 303 & \$ 23,400 \\ 55(t i e d) & \text { Cameron Smith } & 303 & \$ 23,400 \\ 57 & \text { Thongchai Jaidee } & 307 & \$ 23,000 \\ \hline \end{array}$$

Using this, write out the regression equation developed in part (d). If a player shot an even par score of 288 for the four rounds, how much would you expect that player to earn?