Pudi Statistics Milestone 4. 100% Answers with the RATIONALE and CONCEPT Indicated.

Pudi Statistics Milestone 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 interpret ...

Pudi Statistics Milestone 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 decreases 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 increases by 0.8 pounds, on average, when the baby's age increases by 1 month. 2 John, the owner of an ice-cream parlor, collects data for the daily sales of ice cream with respect to the daily temperature. If John were to create a scatterplot, all of the following will be characteristics of correlation EXCEPT ___________. • Strength of association between the daily sales and temperature • Amount of daily sales at any given temperature • Direction of association between the daily sales and temperature • Degree of association between the daily sales and temperature 3 Shawna finds a study of American women that had an equation to predict weight (in pounds) from height (in inches): ŷ = -260 + 6.6x. Shawna’s height was 64 inches and her weight was 150 pounds. What is the value of the residual for Shawna's weight and height? • 730 pounds • -12.4 pounds • 162.4 pounds • 12.4 pounds 4 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. 5 Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation. Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance. • Average mileage per vehicle • Average income per household • The number of cars on the road • The number of citizens in the United States 6 Which of the following is a guideline for establishing causality? • Check if the effect is present or absent when the response variable is present or absent. • The experiment performed should be controlled and randomized. • Look for cases where correlation does not exist between the variables. • Do not consider other possible causes. 7 Which of the following scatterplots shows a correlation affected by inappropriate grouping? • • • • 8 This scatterplot shows the performance of an electric motor using the variables speed of rotation and voltage. Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot. • Form: The data points appear to be in a straight line. Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are closely concentrated. • Form: The data points are arranged in a curved line. Direction: The speed of rotation increases with an increase in voltage. Strength: The data points are far apart from each other. • 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. 9 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. • Slope = -0.35 y-intercept = 10.9 • Slope = -0.35 y-intercept = -10.9 • Slope = 0.35 y-intercept = -10.9 • Slope = 0.35 y-intercept = 10.9 10 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: Voltage Response variable: Thermocouple performance • Explanatory variable: Temperature Response variable: Voltage • Explanatory variable: Voltage Response variable: Temperature • Explanatory variable: Temperature Response variable: Thermocouple performance 11 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? • 13 inches • 12 inches • 14 inches • 11 inches 12 A bank manager declares, with help of a scatterplot, that the number of health insurances sold may have some association with the number of inches it snows. How many policies were sold when it snowed 2 to 4 inches? • 240 • 350 • 470 • 210 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. • 0.85 • 0.92 • 1.00 • 0.71 14 A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be __________. • between 1 and 2 • between 0 and 1 • between -1 and -2 • between 0 and -1 15 This scatterplot shows the number of hours a student slept every night and his or her grade point average. The equation for the least-squares regression line to this data is: ŷ = 0.375x + 1.33. What is the predicted GPA for a student who sleeps 2.5 hours per day? Answer choices are rounded to the hundredths place. • 2.08 • 2.64 • 2.27 • 2.46 16 For this scatterplot, the r2 value was calculated to be 0.9382. Which of the following set of statements is true? • About 94% of the variation in daily temperature can be explained by a positive linear relationship with beach visitors. The correlation coefficient, r, is 0.880 • About 94% of the variation in beach visitors is explained by a negative linear relationship with daily temperatures. The correlation coefficient, r, is 0.969. • There is no strong correlation in the linear association between beach visitors and daily temperatures. The correlation coefficient, r, is 0.880 • About 94% of the variation in beach visitors can be explained by a positive linear relationship with daily temperature. The correlation coefficient, r, is 0.969. 17 Which of the following scatterplots shows an outlier in the y-direction? • • • • Which of the following statements is TRUE? • The researchers proved that exercise causes weight loss. • 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.