STATS Practice HW problems chapter 6

A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet) of 135 homes. A regression analysis was performed to predict the amount of electricity used (in kilowatt-hours) based on size. Assume a linear model is appropriate. Do you think the slope of the regression line will be positive or negative? Why?

Positive, Larger homes should use more electricity

A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet) of 135 homes. A regression to predict the amount of electricity used (in kilowatt-hours) based on size was performed. Assume a linear model is appropriate. What are the variables and units in this regression?

Amount of electricity used (in kilowatt-hours) is Y and size (in square feet) is x.

A regression line for predicting the selling prices of homes in Chicago is

y^=168+102x" class="Wirisformula" role="img" height="26" width="96" alt="y with hat on top equals 168 plus 102 x" style="box-sizing: border-box; -webkit-tap-highlight- border: 0px; max-width: 100%; height: auto; display: inline; vertical-align: -8px; line-height: inherit;">

where x is the square footage of the house. Interpret the residual for a house with 1800 square feet that recently sold for $200,000

The house sold for $16,232 more than was to be expected from the regression equation.

A study of consumer behavior finds a positive correlation between sales of ice cream and sales of soda. What might explain the strong correlation?

Outdoor temperature

For 14 baseball teams, the correlation with number of wins in the regular season is 0.51 for shutouts, 0.61 for hits made, -0.70 for runs allowed, and -0.56 for home runs allowed. Which variable has the strongest linear association with the number of wins?

Runs Allowed

For a summer baseball league, the equation that predicts the number of wins (y) using the number of runs allowed (x) is

y^=80.98-0.108x" class="Wirisformula" role="img" height="26" width="124" alt="y with hat on top equals 80.98 minus 0.108 x" style="box-sizing: border-box; -webkit-tap-highlight- border: 0px; max-width: 100%; height: auto; display: inline; vertical-align: -8px; line-height: inherit;">

What is the predicted number of wins for a team that allowed 80 runs? Round your answer to the nearest integer.

72

If a positive association exists between two quantitative variables

The slope of the regression line will be positive

If a positive association exists between two quantitative variables

As x increases, Y tends to increase

Suppose you were to collect data for the pair of given variables in order to make a scatterplot. For the variables time spent on homework before an exam and the exam grade, which is more naturally the response variable and which is the explanatory variable?

Time spent on homework: explanatory variable

Exam grade: response variable

The August precipitation (in inches) and longitude (in degrees) was plotted for 50 American cities. A linear pattern was observed.

A regression line to predict August precipitation was computed to be:

y^=8.128-0.054x" class="Wirisformula" role="img" height="26" width="124" alt="y with hat on top equals 8.128 minus 0.054 x" style="box-sizing: border-box; -webkit-tap-highlight- border: 0px; max-width: 100%; height: auto; display: inline; vertical-align: -8px; line-height: inherit;">

Use the equation to predict Allendale's rainfall. (Allendale, MI has a longitude of 85.96 degrees.)

3.49 inches

The August precipitation (in inches) and longitude (in degrees) was plotted for 50 American cities. A linear pattern was observed.

A regression line to predict August precipitation was computed to be:

y^=8.128-0.054x" class="Wirisformula" role="img" height="26" width="124" alt="y with hat on top equals 8.128 minus 0.054 x" style="box-sizing: border-box; -webkit-tap-highlight- border: 0px; max-width: 100%; height: auto; display: inline; vertical-align: -8px; line-height: inherit;">

Allendale's August precipitation was 3.69 inches. 

Use the equation to find the residual for Allendale's August rainfall. (Allendale, MI has a longitude of 85.96 degrees.)

0.2 inches

The closer r is to 0, the weaker is the linear association between the variables

true

The correlation between the total box office receipts of the winner for best picture and the total number of nominations won is 0.49 for the best picture winners over a period of 16 years. Assuming the association is linear, describe the association

Moderate, positive, linear association

The regression equation predicting the weight in pounds of an orangutan (y) based on the orangutan's height in inches (x) is given by:

y-hat= -172.68 + 4.842x

Describe the correlation between height and weight based on the slope of the regression line.

Positive correlation since the slope is positive

The regression equation predicting the weight in pounds of an orangutan (y) based on the orangutan's height in inches (x) is given by:

y-hat= -172.68 + 4.842x

Interpret the slope of the regression line.

For every one inch increase in height, the predicted weight increases by 4.842 pounds.

The statistic measuring the strength of the linear relationship between two quantitative variables is the

correlation

The value of the correlation is always between 0 and 1

false

Which of the following displays can be used to visualize the relationship between two quantitative variables?

Scatterplot

Which of the following is NOT a property of R?

r measured the strength of any kind of relationship between x and y

Would you expect the following pair of variables measured for 200 individuals aged 18-32 to have a positive association, negative association, or no association:

Amount of time spent exercising per week and height.

No association