Extra Credit – Statistics

Extra Credit – Statistics

Extra Credit – Statistics

 

 

  • Malaria is a leading cause of infectious disease and death worldwide.  It is also a popular example of a vector-borne disease that could be greatly affected by the influence of climate change. The scatterplot shows total precipitation (in mm) in select cities in West Africa on the x-axis and the percent of people tested positive for malaria in the select cities on the y-axis in 2000.

 

 

  1. There is a strong linear relationship between percentage of people who tested positive for malaria and precipitation: TRUE or FALSE.
  2. There are influential points in the scatterplot: TRUE or FALSE.
  • The correlation between precipitation and percent tested positive for malaria is probably close to zero: TRUE or FALSE.

 

  • Give a truth value to each of the following statements.
 
When calculating the correlation, r, it is important to make sure y is the explanatory variable and the x is the response variable.___________
When calculating the correlation, r, it is important to make sure x is the explanatory variable and the y is the response variable.____________
None of the above.____________
The correlation, r, measures the strength of the linear relationship between two quantitative variables.____________
The correlation, r, measures the strength of the linear relationship between two categorical variables.____________
The correlation, r, measures the strength between one quantitative variable and one categorical variable.______________

 

3-                  A study found a correlation of r = –0.61 between the gender of a worker and his or her income.  Determine whether each of the following conclusions regarding this correlation coefficient is true or false.
Women earn more than men on the average. __________
Women earn less than men on the average. ___________
An arithmetic mistake was made.  Correlation must be positive. __________

 

4-                  Match the four graphs labeled A, B, C, and D, with the following four possible values of the correlation coefficient: –0.9, –0.7, 0.4, 0.95. Assume all four graphs are made on the same scale.
 
 

 

  • In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line.

 

price = –6677 + 175 × horsepower

 

Based on the least-squares regression line, what would we predict the cost to be of a 1991 model car with horsepower equal to 200? _____________

 

  • John’s parents recorded his height at various ages between 36 and 66 months. Below is a record of the results:
Age (months)3648546066
Height (inches)3438414345

 

Which of the following is the equation of the least-squares regression line of John’s height on age?  (Note:  You do not need to directly calculate the least-squares regression line to answer this question.)
(A) Height = 12 ´ (Age)
(B)  Height = Age/12
         (C) Height = 60 – 0.22 ´ (Age)
(D) Height = 22.3 + 0.34 ´ (Age)

 

7-                 John’s parents decide to use the least-squares regression line of John’s height on age to predict his height at age 21 years (252 months).  What conclusion can we draw?
(A) John’s height, in inches, should be about half his age, in months.
(B)  The parents will get a fairly accurate estimate of his height at age 21 years, because the data are clearly correlated.

(C)   Such a prediction could be misleading, because it involves extrapolation.

(D)  All of the above

 

  • In the National Hockey League a good predictor of the percentage of games won by a team is the number of goals the team allows during the season. Data were gathered for all 30 teams in the NHL and the scatterplot of their Winning Percentage against the number of Goals Allowed in the 2006/2007 season with a fitted least-squares regression line is provided:

The least-squares regression line and  were calculated to be

Winning Percent (%) = 116.95 – 0.26  Goals Allowed

= 0.69

Which of the following provides the best interpretation of the slope of the regression line?

  • If the Winning Percent increases by 1%, then the number of Goals Allowed decreases by 0.26.
  • If a team were to allow 100 goals during the season, their Winning % would be 90.95%.
  • If Goals Allowed increases by one goal, the Winning % increases by 0.26%.
  • If the Winning % increases by 1%, then the number of Goals Allowed increases by 0.26
  • If Goals Allowed increases by one goal, the Winning % decreases by 0.26%

 

  • Refer to question 8. The correlation coefficient is ___________.

 

 
 

10-             Refer to question 8 . Fill in the blank: The Montréal Canadiens team allowed 251 goals in 2006/2007. Using the least-squares regression line, the prediction of the team’s Winning Percent would be _________%.

(A) For the Winning Percent and Goals Allowed least-squares regression analysis above, which of the following statements is (are) TRUE?
(B)  About 69% of the variation in the variable Goals Allowed can be explained by the least-squares regression of Winning Percent on Goals Allowed.
(C)  About 69% of the variation in the variable Winning Percent can be explained by the least-squares regression of Winning Percent on Goals Allowed.
(D) If the correlation between Winning Percent and Goals Allowed were calculated it would be 0.83.

 

  • A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be

 

amount of eroded soil = 0.4 + 1.3 ´ (flow rate)

 
One of the flow rates used by the researcher was 0.5 liters per second and for this flow rate the amount of eroded soil was 0.92 kilograms.  These values were used in the calculation of the least-squares regression line.  What is the residual corresponding to these values? _________________

 

 

 

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