Sophia Introduction to Statistics Unit 4 Milestone 4.

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UNIT 4 — MILESTONE 4 - HEADMAN Score 15/18 You passed this Milestone 15 questions were answered correctly. 3 questions were answered incorrectly. 1 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.  1.00  0.85  0.71  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 2. 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.  $6.25 / lb.  $7.75 / lb.  $4.00 / lb.  $0.13 / 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 3. 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. Which answer choice correctly indicates the explanatory and response variables for the scatterplot?  Explanatory variable: Cost Response variable: Distance  Explanatory variable: Distance Response variable: Cost  Explanatory variable: Minneapolis Response variable: Miles flown  Explanatory variable: Miles flown Response variable: Minneapolis 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 4 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 ŷ = 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 the baby's age increases by 1 month.  The weight of a baby decreases by 17 pounds, on average, when the baby's age increases by 1 month.  The weight of a baby increases by 17 pounds, on average, when the baby's age increases by 1 month.  The weight of a baby decreases by 0.8 pounds, on average, when the baby's age increases by 1 month. 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 month, the outcome (weight) will increase by 0.8 pounds on average. CONCEPT Interpreting Intercept and Slope 5. 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 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.  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. 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. [Show More]

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