Sophia Intro to Statistics Milestone 4

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Arapahoe Community College *

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120`092

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Statistics

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Feb 20, 2024

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N illid UNIT 4 — MILESTONE 4 17/18 1 7/ 1 3 < that’s 4% RETAKE 1 question was answered incorrectly. @ 17 questions were answered correctly. T @ Which of the following scatterplots shows a correlation affected by non-linearity? 0 5 10 15 20 25 30 35 40 45 50

oD illid UNIT 4 — MILESTONE 4 17/18 30 s 25 20 [ ] ° ° e ° ° o o 10 i . [ J [ J 5 0 \ 0 5 10 15 20 25 30 35 40 45 50 50 45 |- 40 35 ® ® [ J [ J 30 * - @ 25 O t o | 20 o ° [ 15 ® t ® [ J 10 | | | e ° . o 5 . - 0 0 5 10 15 20 25 30 35 40 45 50 Recall that correlation is for linear association, so if a graph shows curvature, then it would not be adequately captured by using correlation. This plot clearly shows a non-linear graph. CONCEPT — Cautions about Correlation Report an issue with this question 2 @ For the data plotted in the scatterplot, the r2value was calculated to be 0.9846.

oD illid UNIT 4 — MILESTONE 4 17/18 N o @ o o o | | | | | 9] o1 o1 o e w H o O Yearly income (in thousand dollars) w H o ol ® | NN o u | | | | - o1 @ 0 15 20 25 30 35 40 45 50 55 60 65 70 Age Which of the following sets of statements is true? 98.5% of the variation in yearly income is explained by a linear relationship with age. The correlation coefficient, r, is 0.992 98.5% of the variation in age is explained by a nonlinear relationship with yearly income.

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oD illid UNIT 4 — MILESTONE 4 17/18 98.5% of the variation in age is explained by a linear relationship with yearly income. The correlation coefficient, r, is 0.969. 98.5% of the variation in yearly income is explained by a nonlinear relationship with age. O The correlation coefficient, r, is 0.992. RATIONALE The coefficient of determination measures the percent of variation in the outcome, y, explained by the regression. So a value of 0.9846 tells us the regression with age, x, can explain about 98.5% of the variation in income, . We can also note thatr = CONCEPT — Coefficient of Determination/r*2 Report an issue with this question 3 @ A basketball player recorded the number of baskets he could make depending on how far away he stood from the basketball ‘ A

oD illid UNIT 4 — MILESTONE 4 17/18 S Number of Baskets Distance from Net Using the best-fit line, approximately how many baskets can the player make if he is standing ten feet from the net? O 3 baskets O O baskets O 8 baskets © O 5 baskets RATIONALE To get a rough estimate of the number of baskets made when standing 10 feet from the net, we go to the value of 10 on the horizontal axis and then see where it falls on the best-fit line. This looks to be about 5 baskets.

oD illid UNIT 4 — MILESTONE 4 17/18 4 Which of the following scatterplots best shows an outlier in ONLY the y-direction? Number of Hours of Sleep vs. Test Results Test Scores ol o o 1 2 3 4 5 6 7 8 9 10 Number of Hours of Sleep Number of Hours of Sleep vs. Test Results 90 | ' ' ' ' 7:7.’7 ® (] ® Test Scores Ul o o 1 2 3 4 5 6 7 8 9 10 Number of Hours of Sleep Number of Hours of Sleep vs. Test Results o 000 Test Scores ul o o 1 2 3 4 5 6 7 8 9 10 Number of Hours of Sleep

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oD illid UNIT 4 — MILESTONE 4 17/18 o 1 2 3 4 5 6 7 8 9 10 Number of Hours of Sleep RATIONALE To have an outlier in only 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, but also well within the range of x values. CONCEPT — Outliers and Influential Points 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 ferret weighs 2.1 pounds and costs $3.40 per week to feed, while a Labrador Retriever weighs 70 pounds and costs $7.50 per week to feed. Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth. 17 . O $1.73/1b O $1.62 / Ib.

N illid UNIT 4 — MILESTONE 4 17/18 O PTO. IO 7 1T, RATIONALE In order to get slope, we can use the formula: Using the information provided, the two points are: (21 Ib., $3.40) and (70 Ib., $7.50). We can note that: CONCEPT — Linear Equation Algebra Review Report an issue with this question 6 @ Shawna finds a study of American women that has an equation to predict weight (in pounds) from height (in inches). y =-260 + 6.6x. Shawna's mom’s height is 68 inches and her weight is 179 pounds. What is the residual of weight and height for Shawna's mom? 9.8 pounds O P 188.8 pounds O P

oD illid UNIT 4 — MILESTONE 4 17/18 O J& 17T JUUTTUO RATIONALE Recall that to get the residual, we take the actual value - predicted value. So if the actual height of 68 inches and the resulting actual weight is 179 pounds, we simply need the predicted weight. Using the regression line, we can say: The predicted weight is 188.8 pounds. So the residual is: CONCEPT — Residuals Report an issue with this question 7 @ This scatterplot shows the maintenance expense for a truck based on its years of service.

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oD illid UNIT 4 — MILESTONE 4 17/18 SUV O [ = S 400 ® o = i ® 7 g 300 P ® o O C © c 9 200 o c @ = 100 0 Age of Truck (in years) The equation for least regression line to this data setis y = 76.82x + 88.56. What is the predicted value (in dollars) for maintenance expenses when a truck is 7 years old?

oD illid UNIT 4 — MILESTONE 4 17/18 CONCEPT — Predictions from Best-Fit Lines Report an issue with this question 8 @ The scores of the quizzes of five students in both English and Science are: English Science Student 1 6 8 Student 2 5 5 Student 3 9 6 Student 4 4 7 Student 5 8 9 For English, the mean is 6.4 and the standard deviation is 2.0. For Science, the mean is 7 and the standard deviation is 1.6. Using the formula below or Excel, find the correlation coefficient, r, for this set of scores. Answer choices are rounded to the nearest hundredth.

oD illid UNIT 4 — MILESTONE 4 17/18 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(". A B C 1 | English Science 2 | 6 8 3 | 5 5 4 9 6 S | 4 7 6 8 9 7 } 8 |=CORREL(B2:B6,C2:C6) A B C 1 | TEninsh ‘Science 2 6 8 3 5 5 4 9 6 5 | 4 7 6 8 9 7 8 02287479

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oD illid UNIT 4 — MILESTONE 4 17/18 ° @ Data for weight (in pounds) and age (in months) of babies is entered into a statistics software package and results in a regression equation of y =17 + 0.8x. What is the correct interpretation of the slope if the weight is the response variable and the age is the explanatory variable? The weight of a baby increases by 0.8 pounds, on average, when o O the baby's age increases by 1 month. The weight of a baby decreases by 0.8 pounds, on average, when (O the baby's age increases by 1 month. The weight of a baby increases by 17 pounds, on average, when O the baby's age increases by 1 month. The weight of a baby decreases by 17 pounds, on average, when O the baby's age increases by 1 month.

oD illid UNIT 4 — MILESTONE 4 17/18 e i L L S I S S i I g G’ Bt -_————rr—errrw equation we can note as x (age) increases by 1 month, the outcome (weight) will increase by 0.8 pounds on average. CONCEPT — Interpreting Intercept and Slope Report an issue with this question 10 @ For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place. Slope = 0.35 © O y-intercept =10.93 Slope =0.14 O y-intercept =12.65

oD illid UNIT 4 — MILESTONE 4 17/18 Slope =0.14 y-intercept = 6.27 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 1 @

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oD illid UNIT 4 — MILESTONE 4 17/18 () causation. Only a correlation of O implies O causation. High correlation does not always (- O imply causation. Only a correlation of 1 implies O causation. RATIONALE Recall that correlation doesn't imply causation. Causation is a direct change in one variable causing a change in some outcome. Correlation is simply a measure of association. lItis required for causation, but alone does not mean something is causal. CONCEPT — Correlation and Causation Report an issue with this question 2 @ 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.

oD illid UNIT 4 — MILESTONE 4 17/18 1c5S. Identify the confounding variable that is causing Alice's observed association. Parents' income O O The number of free lunches O available The number of bike helmets O available School fundin O g 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 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

oD illid UNIT 4 — MILESTONE 4 17/18 using the variables speed of rotation and voltage. Performance of an Electric Motor 3000 2800 2700 | 2600 | | | e 2500 2400 2300 Speed of Rotation (in RPMs) 2200 2100 2000 O O O & O © A S Voltage (in mV) Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot. O ©

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oD illid UNIT 4 — MILESTONE 4 17/18 O increases with an increase in voltage. Strength: The data points are closely concentrated. Form: The data points appear to be in a straight line. Direction: The voltage increases as the speed of rotation increases. Strength: The data points are closely concentrated. Form: The data points are arranged in a curved line. Direction: The voltage increases as the speed of rotation increases. Strength: The data points are far apart from each other. Form: The data points are arranged in a curved line. Direction: The speed of rotation increases with an increase in voltage.

oD illid UNIT 4 — MILESTONE 4 17/18 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 14. Raoul lives in Minneapolis and he is planning his spring break trip. He creates the scatterplot below to assess how much his trip will cost. Cost of Airplane Ticket vs Miles Flown 700 o __ 525 & (© 3 o o °° ° S o £ 350 o - o 3 o O o 175 o 0 0 750 1500 2250 3000 Distance from MSP (in miles) Which answer choice correctly indicates the explanatory and response variables for the scatterplot? -

N illid UNIT 4 — MILESTONE 4 17/18 Explanatory variable: Cost O Response variable: Distance Explanatory variable: Minneapolis O L Response variable: Miles flown Explanatory variable: Distance © O Response variable: Cost RATIONALE The explanatory variable is what is along the horizontal axis, which is distance. The response variable is along the vertical axis, which is cost. CONCEPT — Explanatory and Response Variables Report an issue with this question 15 @ Rhonda is wondering if there is an association between the number of hours she studies per week and the number of semester credits she is enrolled in. The information is shown in the table below.

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oD illid UNIT 4 — MILESTONE 4 17/18 Study-Hours 0 2 4 6 8 10 12 Number of Semester Credits If Rhonda is taking four credits for the fall semester, how many hours per week will she study? O 8 O 2 O 5 © o° RATIONALE

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oD illid UNIT 4 — MILESTONE 4 17/18 - w’ | U W i || — Scatterplot Report an issue with this question 6 @ A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be between -1 and -2 O between O and -1 O O between 1 and 2 O between O and 1 O 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 O and -1. CONCEPT — Positive and Negative Correlations

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oD illid UNIT 4 — MILESTONE 4 17/18 17 @ Which of the following is a guideline for establishing causality? Do not consider other possible O causes. Look for cases where correlation O does not exist between the variables. Check if the effect is absent when the response variable is present. The experiment performed should be controlled and ®© O | randomized. RATIONALE Finding an association inside an experimental design controls for many other outside influences and helps to ensure that an explanatory variable always precedes the response. This helps to support, with strong confidence, that the association is causal. CONCEPT — Establishing Causality

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oD illid UNIT 4 — MILESTONE 4 17/18 3 @ Which statement about correlation is FALSE? Correlation between the O variables of the data set can be measured. The correlation of a data set can O be positive, negative, or O. Correlation is used to define the variables of only non-linearly © O related data sets. Correlation is the degree to O which the two variables of a data set resemble each other. RATIONALE Recall that correlation is used for linear association between 2 quantitative variables, NOT for non-linearly related variables. CONCEPT — Correlation Report an issue with this question

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oD illid UNIT 4 — MILESTONE 4 17/18 About Contact Us Privacy Policy Cookie Policy Terms of Use © 2024 SOPHIA Learning, LLC. SOPHIA is a registered trademark of SOPHIA Learning, LLC. Your Privacy Choices

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Sophia Intro to Statistics Milestone 4

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