Video Transcriptthis question wants us to find the correlation between height and arm span, which is our now, just from this regression equation, we cannot find the exact value because these regression equations are not absolutely perfect. However, we can't know one thing because the slope is positive. That means that when X goes up, why goes up so the two of them positively correlated. So we know that the correct answer is that R is greater than zero, and we are done. Show Question: Video Answer: Get the answer to your homework problem. Try Numerade free for 7 days We don’t have your requested question, but here is a suggested video that might help. Related QuestionBy looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is (a) greater than zero. (b) less than zero. (c) 0.93 . (d) 6.4 (e) Can't tell without seeing the data.
DiscussionYou must be signed in to discuss. Video TranscriptWe cannot find the exact correlation between height and arm span because the regression equations are not perfect. The slope is positive and we don't know anything. When X goes up, why goes up so the two of them correlate. We know that the correct answer is greater than zero. Get More Help with this Textbook
Study Groups Study with other students and unlock Numerade solutions for free. Try Now Top Intro Stats / AP Statistics EducatorsIntro Stats / AP Statistics CoursesLectures Join Course You have data for many years on the average price of a barrel of oil and the average retail price of a gallon of unleaded regular gasoline. If you want to see how well the price of oil predicts the price of gas, then you should make ascatterplot with ______ as the explanatory variable. (a) the price of oil the price of oil In a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gas, you expect to see a strong positive association If women always married men who were 2 years
older than themselves, what would the correlation between the ages of husband and wife be? 1 4. The figure below is a scatterplot of reading test scores against IQ test scores for 14 fifth‐grade children. There is one low outlier in the plot. The IQ and reading scores for this child are (a) IQ = 10, reading = 124. IQ = 124, reading =10 If we leave out the low outlier, the correlation for the remaining 13 points in the figure below is closest to 0.5 The figure below is a scatterplot of reading test scores against IQ test scores for 14 fifth‐grade children. The line is the least‐squares regression line for predicting reading score from IQ score. If another child in this class has IQ score 110,you predict the reading score to be close to (a) 50. 60 The slope of the line in the figure below is closest to (a) −1. 1 Smokers don't live as long (on average) as nonsmokers, and heavy smokers don't live as long as light smokers. You perform least‐squares regression on the age at death of a group of male smokers y and the number of packs per day they smoked x. The slope of your regression line will be less than 0 Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm). .93 Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm). 99.4 Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm). greater than zero Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm). 95% of the variation in height is accounted for by the regression line. Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm). -3.2 A school guidance counselor examines the number of extracurricular activities that students do and their grade point average. The guidance counselor says, "The evidence indicates that the correlation between the number of extracurricular activities a student participates in and his or her grade point average is close to zero." A correct interpretation of this statement would be that (a) active students tend to be students with poor grades, and vice versa. there is no linear relationship between number of activities and grade point average for students at this school. The British government conducts regular surveys of household spending. The average weekly household spending (in pounds) on tobacco products and alcoholic beverages for each of 11 regions in Great Britain was recorded. A scatterplot of spending on alcohol versus spending on tobacco is shown
below. Which of the following statements is true? The observation in the lower‐right corner of the plot is influential for the least‐squares line. The fraction of the variation in the values of y that is explained by the least‐squares regression of y on x is the square of the correlation coefficient. An AP Statistics student designs an experiment to see whether today's high school students are becoming too calculator dependent. She prepares two quizzes, both of which contain 40 questions that are best done using paper‐and‐pencil methods. A random sample of 30 students participates in the experiment. Each student takes both quizzes—one with a calculator and one without—in a random order. To analyze the data, the student constructs a scatterplot that displays the number of correct answers with and without a calculator for each of the 30 students. A least‐squares regression yields the equation Which of the following statements is/are true? I only Scientists examined the activity level of fish at 7 different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are given below. Notice that the horizontal axis on the residual plot is labeled "predicted (F/T)." What was the activity level rating for the fish at a temperature of 20.4°C? 83 Scientists examined the activity level of fish at 7 different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are given below. Notice that the horizontal axis on the residual plot is labeled "predicted (F/T)." Which of the following gives a correct interpretation of s in this setting? The average distance of the activity level ratings from the least‐squares line is about 4.785 units. Which of these is not true of the correlation r between the lengths in inches and weights in pounds of a sample of brook trout? r is measured in inches. When we standardize the values of a variable, the distribution of standardized values has mean 0 and standard deviation 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least‐squares regression line. Suppose the slope of the least‐squares regression line is −0.44. We may conclude that the correlation will also be −0.44. There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least‐squares fit of some data collected by a biologist gives the model
predicted y=25.2+3.3x ,where x is the number of chirps per minute and y is the estimated temperature in degrees Fahrenheit. What is the predicted increase in temperature for an increase of 5 chirps per minute? 16.5 Can you find correlation from least squares regression line?There is a close connection between correlation and the slope of the least square line. It is interesting that the least squares regression line always passes through the point (`x , `y ). The correlation (r) describes the strength of a straight line relationship.
What does the least squares regression line show?Least Squares Regression Line
If the data shows a leaner relationship between two variables, the line that best fits this linear relationship is known as a least-squares regression line, which minimizes the vertical distance from the data points to the regression line.
How is correlation related to least squares regression quizlet?The correlation r is the slope of the least-squares regression line when we measure both x and y in standard units. The square of the correlation r² is the fraction of the variance of one variable that is explained by the least squares regression on the other variable.
How to determine the equation of the least squares regression line?This is true where ˆy is the predicted y-value given x, a is the y intercept, b and is the slope. For every x-value, the Least Squares Regression Line makes a predicted y-value that is close to the observed y-value, but usually slightly off.
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Calculating the Least Squares Regression Line.. |