MAT 135 CH. 4 - Scatter Diagrams
True or false: Correlation implies causation.
False
What is the difference between univariate data and bivariate data?
In univariate data, a single variable is measured on each individual. In bivariate data, two variables are measured on each individual.
The histogram on the right represents the connection time in seconds to an internet provider. Determine which measure of central tendency better describes the "center" of the distribution.
Median.
If the linear correlation between two variables is negative, what can be said about the slope of the regression line?
Negative
A local news broadcast reported that 19% of tickets purchased from the airline are for flights to San Diego. What is wrong with this statement?
No level of confidence is provided along with the estimate.
What does it mean if r=0?
No linear relationship exists between the variables.
Will the following variables have positive correlation, negative correlation, or no correlation? Number of children in the household under the age of 3 and expenditures on diapers
Positive
What does it mean to say that two variables are positively associated? Negatively associated?
Positive: There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases. Negative: There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases.
The mean finish time for a yearly amateur auto race was 185.71 minutes with a standard deviation of 0.306 minute. The winning car, driven by Sam, finished in 185.14 minutes. The previous year's race had a mean finishing time of 112.7 with a standard deviation of 0.124 minute. The winning car that year, driven by Julie, finished in 112.36 minutes. Find their respective z-scores. Who had the more convincing victory?
Sam had a finish time with a z-score of −1.86. Julie had a finish time with a z-score of negative −2.74. Which driver had a more convincing victory? Julie had a more convincing victory because of a lower z-score.
Which variable is likely the explanatory variable and which is the response variable?
The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score.
If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is the response variable. Choose the correct answer below.
The explanatory variable is height and the response variable is head circumference.
Which variable is the explanatory variable based on the goals of the research?
The length of the bear.
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine. (a) Compute the z-score corresponding to the individual who obtained 40.1 miles per gallon. Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the interquartile range, IQR. (d) Determine the lower and upper fences. Are there any outliers?
(a) The z-score corresponding to the individual is 0.33 and indicates that the data value is 0.33 standard deviation(s) above the mean. (b) Determine the quartiles. Q1=36.75 mpg, Q2=38.45 mpg, Q3=41.05 mpg (c) The interquartile range is 4.3 mpg. It is the range of the middle 50% of the observations in the data set (d) The lower fence is 30.3. The upper fence is 47.5. (e) Are there any outliers? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The outlier(s) is/are 49.2.
Is the statement below true or false? The least-squares regression line always travels through the point x,y.
True
What does it mean to say that the linear correlation coefficient between two variables equals 1? What would the scatter diagram look like?
When the linear correlation coefficient is 1, there is a perfect positive linear relation between the two variables. The scatter diagram would contain points that all lie on a line with a positive slope.
The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. (b) Interpret the slope and y-intercept, if appropriate. Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(a) y=−.074x+69.087 (b) For every unit increase in commute time, the index score falls by 0.074, on average. (c) Interpret the y-intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. For a commute time of zero minutes, the index score is predicted to be 69.087. (c) Predict the well-being index of a person whose commute time is 30 minutes. (d) Suppose Barbara has a 15-minute commute and scores 67.2 on the survey. Is Barbara more "well-off" than the typical individual who has a 15-minute commute? Select the correct choice below and fill in the answer box to complete your choice. No, Barbara is less well-off because the typical individual who has a 15-minute commute scores 68.0.
The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon. 24.1, 32.1, 25.7, 33.7, 35.8, 29.4
Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The mean mileage per gallon is 30.13. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The median mileage per gallon is 30.75. Compute the mode miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The mode does not exist.
Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following.
Do the two variables have a linear relationship? The data points do not have a linear relationship because they do not lie mainly in a straight line. If the relationship is linear do the variables have a positive or negative association? The relationship is not linear.
If r=_______, then a perfect negative linear relation exists between the two quantitative variables.
r = -1
Find the sample variance and standard deviation. 18, 11, 3, 6, 9
s^2 = 32.3 s = 5.7
The weight of an organ in adult males has a bell-shaped distribution with a mean of 325 grams and a standard deviation of 25 grams. Use the empirical rule to determine the following. (a) About 95% of organs will be between what weights? (b) What percentage of organs weighs between 250 grams and 400 grams? (c) What percentage of organs weighs less than 250 grams or more than 400 grams? (d) What percentage of organs weighs between 250 grams and 375 grams?
(a) 275 and 375 grams (b) 99.7% (c) 0.3% (d) 97.35%
The accompanying data represent the total compensation for 12 randomly selected chief executive officers (CEO) and the company's stock performance in a recent year. Complete parts (a) through (d) below.
(a) One would think that a higher stock return would lead to a higher compensation. Based on this, what would likely be the explanatory variable? Stock return (c) Determine the linear correlation coefficient between compensation and stock return. r=-.028 (d) Does a linear relation exist between compensation and stock return? Does stock performance appear to play a role in determining the compensation of a CEO? The linear correlation coefficient is close to 0, so no linear relation exists between compensation and stock return. It appears that stock performance plays no role in determining the compensation of a CEO.