Determine the regression equation in y = ax + b form and write it below. A) How many murders per 100,000 residents can be expected in a state with 4.4 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 2.5 thousand automatic weapons? Answer = Round to 3 decimal places.
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Linear Regression Application, Interpolation and Extrapolation
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- Sarah is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees. Employee Presentations New Clients 1 7 2 2 9 3 3 9 4 4 10 3 5 11 5 6 12 3 Sarah would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The expected number of new clients per month for an employee who made 10 presentations per month is ________. 2.3982 1.6753 3.0521 3.4348The head width (in) and weight (lb) is measured for a random sample of 20 bears.The data shows that the mean head width is 6.9 inches, mean weight is 214.3 lb, and thecorrelation r = 0.879 and its p-value is less than 0.0001. The suggested linear regressionequation is WEIGHT = -212 + 61.9 WIDTH.(a) How is the best predicted weight value of a given head width found with this data found?(b) For the preceding part, why?(c) Find the best predicted weight given a bear with a head with of 6.5 inches.The systolic blood pressure dataset (in the third sheet of the spreadsheet linked above) contains the systolic blood pressure and age of 30 randomly selected patients in a medical facility. What is the equation for the least square regression line where the independent or predictor variable is age and the dependent or response variable is systolic blood pressure? Y=__________ X + ______________ Patient 7 is 67 years old and has a systolic blood pressure of 170 mm Hg. What is the residual? __________ mm Hg Is the actual value above, below, or on the line? What is the interpretation of the residual? (difference in actual &predicated bp, difference in age, the amount of systolic changes)
- Suppose we want to predict the price of an external hard drive from its capacity. Use the table below to answer the following questions (source: De Veaux, Intro Stats, 4th Edition).a) Identify the explanatory and the response variable.b) Use your calculator to create a scatterplot. Describe the scatterplot (direction, form, strength, and outliers).c) Use your calculator to determine the correlation coefficient.d) Use your calculator to find the linear regression line. Be sure to use correct notation when writing your answer.e) State the slope and interpret it in the context of the problem.f) According to Amazon, a 20 TB drive was listed at $2017.86. What is the residual for this prediction? Was this an over or an underestimate? Hard Drive Capacity (in TB) Price ( in $) 0.5 57.99 1.0 75.99 2.0 109.99 3.0 105.99 4.0 144.97 6.0 435.55 8.0 587.27 12.0 1073.97 32.0 4505.00Bill is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees. Employee Presentations New Clients 1 2 1 2 8 2 3 9 4 4 10 3 5 11 5 6 12 6 Bill would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The average number of new clients per month for an employee who made 20 presentations per month is ________. 5.02 5.45 3.43 8.69A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.555 Stdev width: 0.914 Mean height: 12.686 Stdev height: 1.634 Correlation coefficient: 0.8203 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.
- Years of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 2 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 9 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methodsIn every class, there are some students who speed through their tests while other students continue working on their tests until the very last second. To investigate whether these behaviours affeci students' scores, a researcher collected data on the amount of time students spend on a test and their grades from that test (N = 15). The researcher saved the results of their study to a file called hw6_exams. cv. Load the data into jamovi and answer the following questions. 1. Conduct a regression analysis predicting exam grade from time spent on the test. Paste the resulting model fit table and model coefficients table here . Make sure you include the F-test in the model fit table. 2. Paste an appropriate graph from jamovi. Make sure it includes a regression line . 3. What is the value of the test statistic for the overall model ? 4. What is the degrees of freedom for the overall model ? 5. What is the precise p-value for the overall model? Make sure you report the value to at least three…A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employee. A sample of 10 employees was chosen, and the following data were collected. A. Is the estimated regression equation appropriate and adequate
- The owner of Showtime Movie Theaters, Inc. would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly GrossRevenue($1000s) TelevisonAdvertising($1000s) NewspaperAdvertising($1000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 Part A: Develop an estimated regression equation with the amount of television advertising as the independent variable. Part B: Develop an estimated regression equation with both television advertising and news paper advertising as independent variables. Part C: Is the estimated regression rquation coefficient for television advertising expenditures the same in part (a) and in part (b) ? Interpret the coefficient in each case. Part D : Predict Weekly gross revenue for a week $3500 is spent on television advertising and $1800 is spent on newspaper advertising? Please hurryIn a certain type of metal test specimen, the normal stress on a specimen is known tobe functionally related to the shear resistance. The following is a set of codedexperimental data on the two variables:Normal stress (X) 26.8 25.4 28.9 23.6 27.7 23.9 24.7Shear resistance (Y) 26.5 27.3 24.2 27.1 23.6 25.9 26.3i) Estimate the linear regression line and interpret regressioncoefficient.ii) Comment about of goodness of fit of the estimated regression line.The table below lists the maximum weights for which one repetition of a half-squat can be performed and times to run a 10-meter sprint for 12 international soccer players. Use technology (StatCrunch or a calculator) to help you answer the following, and round to the nearest hundredth where rounding is necessary. a. Are the variables negatively or positively correlated? b. Find and interpret the correlation coefficient r for the data. c. Find the linear regression line that best fits this data. Write it in y = a + bx form. d. Make predictions about 10-meter sprint times for soccer players who can squat 165 lbs and 250 lbs respectively. Which of these predictions is more reliable and why?