Sophia Introduction to Statistics Unit 4.pdf

Sophia Introduction to Statistics Unit 4 – Milestone 4 (Below is a compilation of all questions for Unit 4 – Milestone 4. The answers are 100% correct, and it guaranteed to earn you a perfect score in this unit. For a faster search, just hit on ctrl f on windows, or command f on mac. Good luck!) You passed this Milestone 18 questions were answered correctly. 1 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 increases by 15 millimeters, on average, when the tadpole's age increases by 1 day. • 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. 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 2 Which of the following scatterplots shows an outlier in the y-direction? SOPHIA INTRODUCTION TO STATISTICS UNIT 4 - MILESTONE 4 •• • • 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 3 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? • 193.2 pounds • 809.2 pounds • -11.2 pounds • 11.2 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 4 For ten students, a teacher records the following scores of two assessments, Quiz 1 and Test. Quiz 1 (x) Test (y) 15 20 12 15 10 12 14 18 10 10 8 13 6 12 15 10 16 18 13 15 Mean 11.9 14.3 Standard Deviation 3.3 3.5 The correlation of Quiz 1 and Test is 0.568. Given the information below, what is the slope and y-intercept for the leastsquares line of the Quiz 1 scores and Test scores? Answer choices are rounded to the hundredths place. • Slope = 0.54 y-intercept = 1.71 • Slope = 0.54 y-intercept = 1.22 • Slope = 0.60 y-intercept = 1.22 • Slope = 0.60 y-intercept = 7.16 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 5 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.