Unit 4 Milestone Statistics

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Strayer University *

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Electrical Engineering

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Jan 9, 2024

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16/18 that's 89% RETAKE 16 questions were answered correctly . 2 questions were answered incorrectly . 1 Which statement about correlation is FALSE?  Correlation is a quantitative measure of the strength of a linear association between two variables.  Correlation is measured by r, the correlation coefficient which has a value between -1 and 1.  A correlation of -1 or 1 corresponds to a perfectly linear relationship.  Correlation is a quantitative measure of the strength of a non-linear association between two variables. RATIONALE Correlation specifically measures the strength and direction of a linear association between two variables. So we can't use it for all variables or for non-linear associations. CONCEPT Correlation Report an issue with this question 2 Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches): ŷ = -210 + 5.6x. Shawna's dad’s height is 72 inches and he weighs 182 pounds. What is the residual of weight and height for Shawna's dad?  -11.2 pounds

 193.2 pounds  11.2 pounds  809.2 pounds RATIONALE Recall that to get the residual, we take the actual value - predicted value. So if the actual height of 72 inches and the resulting actual weight is 182 pounds, we simply need the predicted weight. Using the regression line, we can say: The predicted weight is 193.2 pounds. So the residual is: CONCEPT Residuals Report an issue with this question 3 The scatterplot below shows the relationship between the grams of fat and total calories in different food items. The equation for the least-squares regression line to this data set is . What is the predicted number of total calories for a food item that contains 25 grams of fat?  383.55

 483.55  417.56  549.54 RATIONALE In order to get the predicted calories when the grams of fat is equal to 25, we simply substitute the value 25 in our equation for x. So we can note that: CONCEPT Predictions from Best-Fit Lines Report an issue with this question 4 A scientist is comparing parts of the body. The tibia length is plotted against the body length as shown below. Using the best-fit line, approximately how long would the tibia bone be if the body length is 62 inches?  11 inches  12 inches  13 inches  14 inches RATIONALE

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To get a rough estimate of the length of the tibia when the body length is 62 inches, we go to the value of 62 on the vertical axis and then see where it falls on the best-fit line. This looks to be about 12 inches. CONCEPT Best-Fit Line and Regression Line Report an issue with this question 5 Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed. Using weight as the explanatory variable, what is the slope of a line between these two points? Answer choices are rounded to the nearest hundredth.  $4.00 / lb.  $0.13 / lb.  $7.75 / lb.  $6.25 / lb. RATIONALE In order to get slope, we can use the formula: . Using the information provided, the two points are: (0.5 lb., $2) and (62.5 lb., $10). We can note that: CONCEPT Linear Equation Algebra Review

Report an issue with this question 6 This scatterplot shows the performance of a thermocouple using the variables temperature difference and voltage. Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot.  Form: The data pattern is nonlinear. Direction: There is a negative association between temperature difference and voltage. Strength: The data pattern is weak.  Form: The data pattern is linear. Direction: There is a negative association between temperature difference and voltage. Strength: The data pattern is strong.  Form: The data pattern is linear. Direction: There is a positive association between temperature difference and voltage. Strength: The data pattern is strong.  Form: The data pattern is nonlinear. Direction: There is a positive association between temperature difference and voltage. Strength: The data pattern is weak.

RATIONALE If we look at the data, it looks as if a straight line captures the relationship, so the form is linear. The slope of the line is positive, so it is increasing. Finally, since the dots are closely huddled around each other in a linear fashion, it looks strong. CONCEPT Describing Scatterplots Report an issue with this question 7 The scatterplot below shows the performance of a thermocouple. Which answer choice correctly indicates the explanatory variable and the response variable for the scatterplot?  Explanatory variable: Temperature Response variable: Thermocouple performance  Explanatory variable: Temperature Response variable: Voltage  Explanatory variable: Voltage Response variable: Thermocouple performance  Explanatory variable: Voltage Response variable: Temperature RATIONALE The explanatory variable is what is along the horizontal axis, which is temperature difference. The response variable is along the vertical axis, which is voltage. CONCEPT Explanatory and Response Variables

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Report an issue with this question 8 Which of the following is a guideline for establishing causality?  Do not consider other possible causes.  Keep all variables the same to get duplicate results.  Look for cases where correlation exists between the variables of a scatterplot.  Check if the effect is present when the response variable is absent. RATIONALE Recall that correlation is not sufficient alone to assess causality, however it is necessary. So for something to be causal, it must have a strong association. CONCEPT Establishing Causality Report an issue with this question 9 Which of the following scatterplots shows a correlation affected by inappropriate grouping?     RATIONALE

Since this data has 4 distinct groups, by examining overall correlation by all the data, it will not capture how the data in each group is associated. So overall the correlation might not be very strong, but if we look at correlation inside each group, there would be a much stronger relationship. CONCEPT Cautions about Correlation Report an issue with this question 10 A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be __________.  between 0 and 1  between 1 and 2  between -1 and -2  between 0 and -1 RATIONALE As the number of miles increases more gas is required, so there should be less gas in the tank. This would be a negative relationship and we would expect the value to be between 0 and -1. CONCEPT Positive and Negative Correlations Report an issue with this question 11 Which of the following scatterplots shows an outlier in the y-direction?   

 RATIONALE To have an outlier in the y-direction the outlier must be in the range of x data but outside the range of y-data. This outlier is outside of the data in the y direction, lying below all of the data. CONCEPT Outliers and Influential Points Report an issue with this question 12 Peter analyzed a set of data with explanatory and response variables x and y. He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively. He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively. The correlation was found to be 0.964. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.  Slope = 1.08 y-intercept = -5.38  Slope = 0.86 y-intercept = 5.50  Slope = 1.08 y-intercept = 3.78 

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Slope = 0.86 y-intercept = -2.69 RATIONALE We first want to get the slope. We can use the formula: To then get the intercept, we can solve for the y-intercept by using the following formula: We know the slope, , and we can use the mean of x and the mean of y for the variables and to solve for the y-intercept, . CONCEPT Finding the Least-Squares Line Report an issue with this question 13 The table below shows the grade and reading level for 5 students. Grade Reading Level Student 1 2 6 Student 2 6 14 Student 3 5 12 Student 4 4 10 Student 5 1 4 For grade, the mean is 3.6 and the standard deviation is 2.1. For reading level, the mean is 9.2 and the standard deviation is 4.1. Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices are rounded to the nearest hundredth. 

0.71  1.00  0.85  0.92 RATIONALE In order to get the correlation, we can use the formula: Correlation can be quickly calculated by using Excel. Enter the values and use the function "=CORREL(". CONCEPT Correlation Report an issue with this question 14 In a study of 30 high school students, researchers found a high correlation, 0.93, between amount of exercise and weight lost. Which of the following statements is TRUE?  93% of the high school students studied lost weight.  The researchers proved that exercise causes weight loss, but only for high school students.  There is a strong positive linear association between weight loss and exercise, but the researchers have not proven causation.

 The researchers proved that exercise causes weight loss. RATIONALE Recall that correlation measures the strength and direction of linear association. So r= 0.93 indicates a strong positive linear association. Recall also, that correlation doesn't imply causation. Causation is a direct change in one variable causing a change in some outcome. CONCEPT Correlation and Causation Report an issue with this question 15 Alice reads a scatterplot that shows data for nine schools. It relates the percentage of students receiving free lunches to the percentage of students wearing a bicycle helmet. The plot shows a strong negative correlation. Alice recalls that correlation does not imply causation. In this example, Alice sees that increasing the percentage of free lunches would not cause children to use their bicycle helmets less. Identify the confounding variable that is causing Alice's observed association.  Parents' income  School funding  The number of free lunches available  The number of bike helmets available RATIONALE Recall that a lurking variable is something that must be related to the outcome and explanatory variable that when considered can help explain a relationship between 2 variables. Since higher income for parents is positively related to owning a bike helmet

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and this higher income would mean less free school lunches, this variable would help explain why we see this association. CONCEPT Correlation and Causation Report an issue with this question 16 Data for length of the tail (in millimeters) and age (in days) of tadpoles is entered into a statistics software package and results in a regression equation of ŷ = 15 - 1.5x. What is the correct interpretation of the slope if the length of the tail is the response variable and the age is the explanatory variable?  The length of the tail decreases by 1.5 millimeters, on average, when the tadpole's age increases by 1 day.  The length of the tail decreases by 15 millimeters, on average, when the tadpole's age increases by 1 day.  The length of the tail increases by 1.5 millimeters, on average, when the tadpole's age increases by 1 day.  The length of the tail increases by 15 millimeters, on average, when the tadpole's age increases by 1 day. RATIONALE When interpreting the linear slope we generally substitute in a value of 1. So we can note that, in general, as x increases by 1 unit the slope tells us how the outcome changes. So for this equation we can note as x (age) increases by 1 day, the outcome (length) will decrease by 1.5 millimeters on average. CONCEPT Interpreting Intercept and Slope Report an issue with this question 17 For the plot below the value of r 2 is 0.7783.

Which of the following sets of statements is true?  About 78% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.882.  About 78% of the variation in distance flown can be explained by the ticket price. The correlation coefficient, r, is 0.606.  About 22% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.606.  About 88% of the variation in ticket price can be explained by the distance flown. The correlation coefficient, r, is 0.882. RATIONALE The coefficient of determination measures the percent of variation in the outcome, y, explained by the regression. So a value of 0.7783 tells us the regression with distance, x, can explain about 77.8% of the variation in cost, y. We can also note that r = . CONCEPT Coefficient of Determination/r^2 Report an issue with this question 18 Fred Anderson, an artist, has recorded the number of visitors who visited his exhibit in the first 8 hours of opening day. He has made a

scatter plot to depict the relationship between the number of hours and the number of visitors. How many visitors were there during the fourth hour?  4  21  1  20 RATIONALE The number of visitors at 4 hours is 4 visitors. This is the value that is directly at the value at 4 on the horizontal axis. CONCEPT Scatterplot Report an issue with this question

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