Topics include but are not limited to linear correlation and regression.

1.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

What are the values that form the centroid for this bivariate data:x,y?

Report the value of xhere, without insignificant digits or extra characters:

Report the value ofyhere, without insignificant digits or extra characters:

2.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

Create a scatter plot of this bivariate data.What is the apparent trend?

A.The trend is positive.As the number of staffers at the arena for an event increases, the number of complaints increases correspondingly.

B.The trend is negative.As the number of staffers at the arena for an event decreases, the number of complaints increases correspondingly.

C.There is essentially no trend.Any increase or decrease in the number of staffers apparently has minimal or no impact the number of complaints received.

D.Any trend analysis cannot be completed at this time, based on the available evidence.

3.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

What is the value of the Pearson product moment correlation coefficient,r?Express the answer with sign in decimal form, rounded to the nearest thousandth.

Answer:

4.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

How best or most accurately can the association or correlation evidenced in the data be described?Select the best choice.

The association or correlation is perfect and positive.

The association or correlation is high, very strong and positive.

The association or correlation is strong and positive.

The association or correlation is moderate and positive.

The association or correlation is low or weak but positive.

The association or correlation is very weak, essentially trendless, although perhaps either slightly positive or slightly negative.

The association or correlation is low or weak but negative.

The association or correlation is moderate and negative.

The association or correlation is strong and negative.

The association or correlation is high, very strong and negative.

The association or correlation is perfect and negative.

The association or correlation cannot be determined based on the available evidence.

5.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

What is the equation of the trend or regression line that best represents this data?Express the values in decimal form, rounding the slope and y-intercept to the nearest hundredths when reporting the answers.

Report the slope here, rounded as requested, including its sign to indicate positive or negative trend:

Report they-intercept here, rounded as requested, including its sign:

6.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

What is the value of the coefficient of determination,r²?Express the answer with sign in decimal form, rounded to the nearest thousandth.

Answer:

7.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

What percentage of the variability evidenced between the independent (input) and dependent (output) variables is attributable to the linear regression model?Express the answer rounded to the nearest whole percent with percent symbol.

Answer:

8.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

What percentage of the variability evidenced between the independent (input) and dependent (output) variables isnotattributable to the linear regression model?Express the answer rounded to the nearest whole percent with percent symbol.

Answer:

9.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

If 42 staffers are on duty, predict the number of complaints, according to the model.

Express the answer rounded to the nearest whole complaint.

Answer:

10.After an extended closure for a public health emergency, the management at Metro Arena is reviewing its hospitality for roving ushers, bathroom attendants and other greeters not specifically assigned to monitor seating areas, in anticipation of its reopening.They wondered about the association between the number of these seemingly surplus staffers on duty at an event and the number of past complaints or concerns brought to their attention at the main customer service counter.Some randomly selected data is as follows, where the variablexrepresents the number of these staffers at selected events, and the variableyrepresents the number of complaints or concerns filed during that event.

COMMENTS & HINTS:Use computer and/or calculator technology to your advantage so to minimize tedious calculations!Round as requested, when necessary.

x 37 40 25 45 28

y 24 20 32 16 28

If 25 staffers are on duty, predict the number of complaints, according to the model.

Express the answer rounded to the nearest whole complaint.

Answer: