a) Produce the regression results using Microsoft Excel b) From a, find the following: (i) The Regression equation and interpret the intercept and the slope. (ii) Coefficient of Determination, R? and interpret (iii) Is there a linear relationship between X and Y ? Use the t-test, F-test , the confidence interval of the slope to c) Predict the Y when X is 99.
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- The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: Give the following: a. linear regression line and equation b. computation of the coefficient of determination ?^2 c. Computation of the coefficient of correlation ? d. Estimate the final examination grade of a student who received a grade of 85 on the midterm report.The 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 amount of kerosene used by a typical household in a week (Q, in litres) is found to have a strong correlation with the price of kerosene (P, in $). For 6 observations, the following data was collected:Q P11.4 4.0014 3.5016 3.0018 2.5020. 2.0022 1.50(a) Create a regression relationship for this data.(b) Perform a hypothesis test to determine whether the slope coefficient obtained in part (a) above issignificant. (c) Use the regression equation in part (a) above to predict the quantity of kerosene used by a household when the price is $3.75 per litre. (d) Calculate the price elasticity of demand for kerosene at a price of $3.75 (e) Using a further calculation, discuss how well the regression equation in part (a) above fits the data.(f) Discuss whether the relationship between the price and quantity could be due to the income effect, the substitution effect, or both
- The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.Given the table below, Let y, x1, x2, and x3 be the time of concentration (t, in hr), watershed length (L in ft), watershed slope (S in %), and runoff curve number (CN): Evaluate the linear multiple regression model with two or three predictor variables. Compute the multiple correlation coefficient, the standard error of estimate, and the standard deviation of the variable y. Discuss the reliability of the modelA sample of 40 individuals collects their shoe size and the height (cm) for CSI data. The scatter plot and results from a simple linear regression are recorded: HEIGHT = 126.76238 + 4.8782178 SHOE SIZE Sample size: 40R (correlation coefficient) = 0.77918855P-value < 0.0001 (a) Does the scatterplot and results show a linear correlation between shoe size and height? (b) How can you tell? (c) Will it be appropriate to use the linear regression equation given in the output? (d) Krusty the Clown wears size 8.5 shoes. According to the linear regression equation, how tall is Krusty the Clown? (e) Sideshow Bob wears size 14 shoes. According to the linear regression equation, how tall is Sideshow Bob?
- The amount of gas used by a typical household in a week (Q, in litres) is found to have a strongcorrelation with the price of gas (P, in $). For 6 observations, the following data was collected:Q P11.4 4.0014 3.5016 3.0018 2.5020 2.00(a) Create a regression relationship for this data(b) Perform a hypothesis test to determine whether the slope coefficient obtained in part (a) above is statistically significant(c) Use the regression equation in part (a) above to predict the quantity of gas used by a household when the price is $3.75 per litre(d) Calculate the price elasticity of demand for gas at a price of $3.75 (e) Using a further calculation, discuss how well the regression equation in part (a) above fits the dataA car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 0.203521 The coefficient of determination is 0.234 Test statistic= 0.704 P-value= 0.014 Construct a 95% confidence interval around the sample slope and interpret its meaning. The confidence interval is (__________,_________). (Type an integer or decimal rounded to three decimal places as needed.)A ski resort asked a random sample of guests to rate their satisfaction on various attributes of their visit on a scale of 1–5 with 1 = very unsatisfied and 5 = very satisfied. The estimated regression model was Y = overall satisfaction score, X1 = lift line wait, X2 = amount of ski trail grooming, X3 = safety patrol visibility, and X4 = friendliness of guest services. Predictor Coefficient Intercept 2.7115 LiftWait 0.1474 AmountGroomed 0.2517 SkiPatrolVisibility 0.0656 FriendlinessHosts −0.1172 (a) Write the fitted regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.) yˆy^ = ?? + ?? * LiftWait + ?? * AmountGroomed + ?? * SkiPatrolVisibility + ?? * FriendlinessHosts (b) Interpret each coefficient. Overall satisfaction increases Correctwith an increase in satisfaction for each individual predictor except for friendliness of hosts.(c) Would the intercept seem to have meaning in this…
- A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on the employee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 Predict the sales next month for an employee with 2.5 years of experience. The predicted sales is _________ cars. (Type an integer or decimal rounded to one decimal place as needed.)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 adequateThe accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?