Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA 0.7352 0.5405 0.5205 2130.9497 49
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- A researcher is interested in examining the relationship between spousal abuse and child abuse. Specifically, they are interested in determining whether there is a predictive relationship between spousal abuse and child abuse in 5 county social services offices. Calculate the linear regression line for the following data. Note you have already calculated the first step to this analysis (Pearson's Correlation)Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with an altitude of 6327 ft (or 6.327 thousand feet). Altitude Temperature3 598 3413 2219 -429 -2931 -4134 -58 a. Find the explained variation. (Round to two decimal places as needed.) b. Find the unexplained variation. (Round to five decimal places as needed.) c. Find the indicated prediction interval. __<y<__ (Round to four decimal places as needed.)Togetherness Are good grades in high school associ-ated with family togetherness? A simple random sample of 142 high-school students was asked how many mealsper week their families ate together. Their responses produced a mean of 3.78 meals per week, with a stand-ard deviation of 2.2. Researchers then matched these responses against the students’ grade point averages. Thescatterplot appeared to be reasonably linear, so they went ahead with the regression analysis, seen below. No appar-ent pattern emerged in the residuals plot. Dependent variable: GPAR-squared = 11.0%s = 0.6682 with 142 - 2 = 140 dfVariable Coefficient SE(Coeff)Intercept 2.7288 0.1148Meals/wk 0.1093 0.0263 a) Is there evidence of an association? Test an appropri-ate hypothesis and state your conclusion. b) Do you think this association would be useful inpredicting a student’s grade point average? Explain.c) Are your answers to parts a and b contradictory?Explain.
- A researcher at a large company has collected data on the beginning salary and current salary of 50 randomly selected employees. The correlation between the data sets is r = 0.912. The summary statistics from the data collected are shown bellow: Beginning Salary Ending Salary Mean x¯=56,340 y¯=82,070 Standard deviation Sx = 5,470 Sy = 7,800 Use a complete sentence to describe the strength and direction of the linear relationship between beginning salary and current salary. Find the equation of the least-squares regression line. (Round to two decimal places)A dataset contains data on birth weights of 65535 babies born in June 1997along with variables that are potentially related to birth weights. The sampleis restricted to singleton births, with mothers recorded as either black orwhite, between the ages of 18 and 45, resident in the United States.With the aim to investigate factors influencing the weight of babies atbirth, a regression of W eight on a range of variables has been carried out.A description of variables is given below and the estimation results can befound on the following page.Referring to these results, answer the following questions. Keep in mindthat two of the regressors, Mom_Age and M_W tGain, are entered in theregression in terms of the deviations from their mean. (a) Interpret the estimated interceptA study is conducted in patients with HIV. The primary outcome is CD4 cell count, which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to the use of supplements (coded as 1 = yes and 0 = no) and to the duration of HIV in years (i.e., the number of years between the diagnosis of HIV and the study date). For the analysis, y = CD4 count: = 501.41 + 12.67 Supplements − 30.23 Duration of HIV. What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years? What is the expected CD4 count for a patient not taking supplements who was diagnosed with HIV at study enrollment? What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years? If we compare two patients and one has had HIV for 5 years longer…
- Traffic Highway planners investigated the relationshipbetween traffic Density (number of automobiles per mile)and the average Speed of the traffic on a moderately largecity thoroughfare. The data were collected at the samelocation at 10 different times over a span of 3 months.They found a mean traffic Density of 68.6 cars per mile(cpm) with standard deviation of 27.07 cpm. Overall, the cars’ average Speed was 26.38 mph, with standard devia-tion of 9.68 mph. These researchers found the regression line for these data to be Speed = 50.55 - 0.352 Density.a) What is the value of the correlation coefficientbetween Speed and Density?b) What percent of the variation in average Speed isexplained by traffic Density? c) Predict the average Speed of traffic on the thorough-fare when the traffic Density is 50 cpm. d) What is the value of the residual for a traffic Densityof 56 cpm with an observed Speed of 32.5 mph?e) The data set initially included the point Density =125 cpm, Speed = 55 mph. This…Let's study the relationship between brand, camera resolution, and internal storage capacity on the price of smartphones. Use α = .05 to perform a regression analysis of the Smartphones01CS dataset, and then answer the following questions. When you copy and paste output from MegaStat to answer a question, remember to choose to "Keep Formatting" to paste the text. a. Did you find any evidence of multicollinearity and variance inflation among the predictors. Explain your answer using a VIF analysis. b. Copy and paste the normal probability plot for your analysis. Is there any evidence that the errors are not normally distributed? Explain. c. Copy and paste the Residuals vs. Predicted Y-values. Does the pattern support the null hypothesis of constant variance for the errors? Explain. d. Study the residuals analysis. Which observations, if any, have unusual residuals? e. Study the residuals analysis. Calculate the leverage statistic. Which observations, if any, are high leverage…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
- Zagat’s publishes restaurant ratings for various locations in the United States. The following table contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service. Predict the mean cost per person for a restaurant with a sum-mated rating of 50. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal? Location Food Décor Service Summated Rating Coded Location Cost Bins Midpoints City 22 14 19 55 0 33 19.99 25 City 20 15 20 55 0 26 29.99 35 City 23 19 21 63 0 43 39.99 45 City 19 18 18 55 0 32 49.99 55 City 24 16 18 58 0 44 59.99 65 City 22 22 21 65 0 44 69.99 75 City 22 20 20 62 0 50 79.99 85 City 20 19…Consider the image a plot of a regression line. What do you call the regression line that results in the smallest sum of errors squared? a. correlational lineb. forecasting linec. least squares regression lined. Pearson's line