Correlation_and_Regression

grStudy Guide - Correlation and Regression 1.|Regression is a statistical method used to describe the nature of the relationship between variables.| A)|True| B)|False| 2.|A positive relationship exists when both variables increase or decrease at the same time.| A)|True| B)|False| 3.|__________ is a statistical method used to determine whether a relationship between variables exists.| 4.|In a __________ relationship, as one variable increases, the other variable decreases, and vice versa.| 5.|A study was conducted to determine if there was a linear relationship between a person's age and his/her peak heart rate. Construct a scatter plot and determine what type of relationship there is between a person's age and his/her peak heart rate.Age, |Peak Heart Rate, |16|220|26|194|32|193|37|178|42|172|53|160|48|174|21|214|| 6.|Draw a scatter plot for the following data that show the demand for a product (in hundreds) and its price (in dollars) charged in nine different cities.City|Price, |Demand, |1|23|17|2|18|48|3|19|41|4|21|38|5|20|33|6|25|17|7|22|35|8|17|52|9|22|24|| 7.|An experiment is carried out to determine the relationship between the average speed (rpm) and power (hp) of a mixer. Construct a scatter plot for the data obtained in the experiment.Run|Average Speed, |Power, |1|325.0|1.10|2|348.9|1.40|3|312.9|1.07|4|230.0|0.25|5|269.2|0.64|6|305.0|0.93|| 8.|Determine the type of relationship shown in the figure below.| A)|positive | B)|negative | C)|multiple | D)|There is no relationship. | 9.|Daniel Wiseman, a scientist for Gres-Trans Corp., wants to determine if the flow rate of a particular material changes with different changes in temperature. The data is plotted in the figure below. What type of relationship exists between the flow rate and the change in temperature'| A)|negative | B)|positive | C)|There is no relationship. | D)|curvilinear | 10.|The range of the correlation coefficient is from 0 to 1.| A)|True| B)|False| 11.|The rounding rule for the correlation coefficient uses two decimal places.| A)|True| B)|False| 12.|A correlation coefficient of 0.96 would mean that the values of increase as the values of decrease.| A)|True| B)|False| 13.|The population correlation coefficient is computed by using all possible pairs of data values taken from a population.| A)|True| B)|False| 14.|If there is a strong negative linear relationship between the variables, the value of __________ will be close to –1.| 15.|Which of the following does not explain a possible relationship between variables when the null hypothesis is rejected' | A)|direct cause-and-effect | B)|reverse cause-and-effect | C)|caused by a third variable | D)|negative effect | 16.|Ten pairs of points yielded a correlation coefficient of 0.79. If , which of the following statements is correct if ' (Do not calculate a t-value.) | A)|Because 0.79 is greater than 0.632, the null hypothesis is not rejected. | B)|Because 0.79 is greater than 0.632, the null hypothesis is rejected. | C)|Because 0.79 is greater than 0.602, the null hypothesis is not rejected. | D)|There is no correlation between the variables. | 17.|The formula for the correlation coefficient is __________.| 18.|A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications. Find the value of .Non-member|Member|Price, |Price, |58|32|42|22|46|20|32|16|25|19|75|58|35|34|63|48 || A)|13,251 | B)|93,624 | C)|19,712 | D)|9349 | 19.|A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications. Determine the value of . Non-member|Member|Price, |Price, |58|32|42|22|46|20|32|16|25|19|75|58|35|34|63|48 || A)|13,251 | B)|93,624 | C)|19,712 | D)|9349 | 20.|A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications. What is the value of the correlation coefficient' Non-member|Member|Price, |Price, |58|32|42|22|46|20|32|16|25|19|75|58|35|34|63|48 || A)|0.762 | B)|0.857 | C)|0.679 | D)|0.932 | 21.|Which of the following could not be the value of a correlation coefficient' A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications. Non-member|Member|Price, |Price, |58|32|42|22|46|20|32|16|25|19|75|58|35|34|63|48 || A)|–0.683 | B)|0.197 | C)|1.000 | D)|–1.369 | Use the following to answer questions 22-23: The city of Oakdale wishes to see if there is a relationship between the temperature and the amount of electricity used (in kilowatts). Temp., |Kilowatts, | 73| 680| 78| 760| 85| 910| 98|1,510| 93|1,170| 81| 837| 76| 600| 105|1,800| 22.|Compute the value of the correlation coefficient for the data in the table.| A)|0.981 | B)|0.834 | C)|0.798 | D)|0.938 | 23.|Compute the test value for the data in the table. | A)|8.329 | B)|6.785 | C)|12.353 | D)|9.648 | 24.|A correlation coefficient computed for and is . Using the -test for the correlation coefficient, what are the critical values' | A)|+2.120 | B)|+2.101 | C)|+1.734 | D)|+1.746 | 25.|If a correlation coefficient calculated for and is found to be , what is the test value for the - test' | A)|4.059 | B)|5.736 | C)|2.851 | D)|6.374 | 26.|A regression line can be used to show trends in data.| A)|True| B)|False| 27.|A regression line was calculated as . The slope of this line is: –3.2.| A)|True| B)|False| 28.|When is not significantly different from 0, the best predictor of is the mean of the __________ of .| 29.|The equation of a regression line is . What is the intercept of this line' | A)|–4.6 | B)|3.2 | C)|4.6 | D)|0 | 30.|Using the regression line found in Problem 29, predict the value of when . | A)|1971 | B)|50 | C)|1906 | D)|71 | 31.|Using a regression line of , a value of would result in a predicted value of | A)|True| B)|False| 32.|When the -axis and -axis have been truncated, the -intercept can be used to graph the regression line.| A)|True| B)|False| 33.|What is the equation for the regression line if , , , , and ' | A)|| B)|| C)|| D)| | 34.|What is the value of when , if the equation of the regression line is ' | A)|4.73 | B)|5.29 | C)|34.5 | D)|11.7 | 35.|A psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded. Determine the equation of the regression line and graph the line on a scatter plot. Hours without Sleep, |Number of Mistakes, |32|6|38|8|48|13|24|5|46|7|35|6|30|5|34|8|42|12|| 36.|A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home. Find the equation of the regression line and graph the line on a scatter plot.Size, |Price, |26|235|27|273|41|387|29|253|33|295|34|335|36|395|45|475|22|203|| 37.|If the correlation coefficient is 0.79, what is the explained variation' | A)|37.6% | B)|62.4% | C)|79% | D)|21% | 38.|If the correlation coefficient is 0.93, what is the unexplained variation' | A)|7% | B)|93% | C)|13.5% | D)|86.5% | 39.|The standard error of estimate can be used for constructing a(n) __________ interval about a value.| 40.|The standard error of estimate is the standard deviation of the observed -values about the predicted values.| A)|True| B)|False| 41.|The standard error of estimate is the square root of the unexplained variation.| A)|True| B)|False| 42.|The formula for the coefficient of nondetermination is .| A)|True| B)|False| 43.|A correlation coefficient was calculated to be 0.83. The coefficient of nondetermination would be 0.17.| A)|True| B)|False| 44.|The variation due to chance, found by the formula __________, is called the unexplained variation.| 45.|A correlation coefficient was calculated to be 0.61. The coefficient of determination would be approximately __________.| 46.|The following data list ages of cars (in years) and monthly repair cost. What is the standard error of estimate'Age|Cost|3|25|5|35|7|55|9|50|11|75|14|85 || A)|6.36 | B)|7.34 | C)|8.75 | D)|5.49 | 47.|The symbol used for the multiple correlation coefficient is .| A)|True| B)|False| 48.|A multiple regression line was calculated in which was a student's grade point average and was a student's age. The multiple regression line was calculated as . If a student has a grade point average of 5.9 and is 20 years old, what is the predicted value of ' | A)|387.2 | B)|400.1 | C)|421.6 | D)|615.5 | Answer Key 1.|A| 2.|A| 3.|Correlation | 4.|negative | 5.| There appears to be a negative relationship between age and peak heart rate. | 6.| | 7.| | 8.|A| 9.|C| 10.|B| 11.|B| 12.|B| 13.|A| 14.|r | 15.|D| 16.|B| 17.|| 18.|C| 19.|A| 20.|B| 21.|D| 22.|A| 23.|C| 24.|D| 25.|B| 26.|A| 27.|A| 28.|data values | 29.|C| 30.|B| 31.|B| 32.|B| 33.|A| 34.|D| 35.| | 36.|| 37.|B| 38.|C| 39.|prediction | 40.|B| 41.|A| 42.|A| 43.|B| 44.|| 45.|0.37 | 46.|A| 47.|A| 48.|B|