I attached the homework below.
Name__________________________________Stat 104 Assistant Professor Angela Johnson-ShawOctober 29, 2020 Test #2 Please show all work for full credit. Use the information below for problems 1 – 9. Listed in the table below are the robbery and aggravated assault rates (occurrences per 100,000) for the 12 most populated U.S. cities in 2006: City Robbery (x) Aggravated Assault (y) New York 288 330 Los Angeles 370 377 Chicago 555 610 Houston 548 562 Phoenix 288 398 Philadelphia 749 720 Las Vegas 409 508 San Antonio 180 389 San Diego 171 301 Dallas 554 584 San Jose 112 248 Honolulu 105 169 1.Construct a scatterplot on the graph paper provided. Is there a linear relationship between robbery and aggravated assault. 2.What quadrants have the greatest influence on the data? Explain 3.Estimate the strength of the linear relationship between robbery and aggravated assault. Comment on the linear association between robbery and assault. Is it positive or negative? Weak or strong? 4.Calculate the slope, , and the y-intercept, , of the regression line that fits the data. 5.Calculate the linear regression equation (predicted line of best fit). 6.Calculate the coefficient of determination. 7.How much of the variation in aggravated assault is explained by the linear relationship between aggravated assault and robbery? 8.Is the least squares regression line (predicted line of best fit) a good fit for the data? Explain. 9.Find the predicted aggravated assault rate for a robbery rate of 150. 10.True or False ______________ If the coefficient of determination is positive, then as x increases, y will also increase. 11.Which of the following is described as the typical prediction error? a.s b.SSE c.SSR d. 12.Given the regression equation , find the residual for the value of if the actual y-value is 9.1. 13.Which of the following represents the strongest linear correlation? a.r = -1 b.r = 0 c.r = 1 d. a and c are correct 14.___________________________ consists of using the regression equation to make estimates or predictions based on x-values that are outside the range of the x-values in the data set. a.Regression b.Prediction c.Extrapolation d.Interpolation 15.True or False _____________________ If r is negative, can be either positive or negative. 16.For the following pairs of variables, identify which is the predictor variable and which is the response variable. Number of college degrees and annual salary a.predictor – number of college degrees response – annual salary b.predictor – annual salary response – annual salary c.predictor – number of college degrees response – number of college degrees d.predictor – annual salary response – annual salary 17.For a certain data set the correlation coefficient between X and Y was found to be -0.002. Interpret the meaning of the correlation coefficient. a.X and Y are mildly negatively correlated. b.X and Y are negatively correlated. c.X and Y are uncorrelated. d.X and Y are mildly positively correlated. 18.For a certain data set the correlation coefficient between X and Y was found to be 0.71. Interpret the meaning of the correlation coefficient. a.X and Y are mildly negatively correlated. b.X and Y are negatively correlated. c.X and Y are uncorrelated. d.X and Y are mildly positively correlated. 19.Of the mean, median, and mode, which must be a value that actually appears in the data set? 20.Use the following data for problems 20 – 23. The prices (in dollars) for a sample of personal computers are: 550, 700, 420, 580, 550, 450, 690, 390, 350 Calculate the following: a.Mean ______________ b.Median ______________ c.Mode ______________ d.Midrange ______________ e.Range ______________ f.Variance ______________ g.Standard Deviation ______________ h.Q1______________ i.Q2______________ j.Q3______________ k.IQR______________ 21.Calculate the values that detect outliers (the lower and upper fences).____________________ Are there any outliers? Yes or No __________ If so, state the outlier(s)_____________________________ 22.Construct a boxplot for the data on the graph paper provided. 23.If a computer with a price of $2000 were added to the list, which would be affected more, the mean or the median? Explain 24.A sample of 100 students was asked how many hours per week they spent studying. The following frequency table shows the results. Number of HoursFrequency 1-414 5-934 10-1429 15-1915 20-24 8 a.Approximate the mean time this sample of students spent studying. b.Approximate the standard deviation of the time this sample of students spent studying. 25.A sample has a variance of 16. What is the standard deviation? Use the following information for problems 26 – 29. Suppose that the mean starting salary of social workers in a specific region is $37,480 with a standard deviation of $1,400. 26.Assume that the histogram of starting salaries is approximately bell-shaped. Approximately what percentage of the salaries will be between $34,680 and $40,280? 27.Assume it is not known whether the histogram of starting salaries is bell-shaped. At least what percent of the salaries will be between $34,680 and $40,280? 28.John’s starting salary is $38,180. What is the z-score of his salary? 29.Find the coefficient of variation of the salaries. 30.True or False ___________ If a student’s exam grade is on the 55th percentile, then approximately 45% of the scores are below his or her grade.