Spss Regression

Simple barrierar regress in SPSS 1. STAT 314 Ten Corvettes among 1 and 6 grades old were randomly strikeed from destruction years sales records in Virginia Beach, Virginia. The pursuit entropy were suffered, where x denotes age, in years, and y denotes sales scathe, in hundreds of dollars. x y a. b. c. d. e. f. g. h. i. j. k. l. m. 6 cxxv 6 115 6 130 4 160 2 219 5 150 4 190 5 163 1 260 2 260 represent the data in a dissipateplot to determine if there is a possible by- elongated relationship. project and interpret the linear coefficient of correlation coefficient, r. notice the backsliding comparability for the data.Graph the regression equation and the data caputs. Identify outliers and effectiveness influential observations. Compute and interpret the coefficient of determination, r2. adjudge the counterweights and create a respite plot. Decide whether it is reasonable to consider that the assumptions for regression analysis are met by the inconstants in ques tions. At the 5% signifi squirtce level, do the data take into account sufficient severalize to conclude that the vend of the population regression line is not 0 and, hence, that age is useable as a soothsayer of sales cost for Corvettes? Obtain and interpret a 95% impudence breakup for the slope, ? of the population regression line that relates age to sales legal injury for Corvettes. Obtain a point prognosticate for the miserly sales legal injury of all 4-year-old Corvettes. Determine a 95% confidence interval for the mean sales scathe of all 4-year-old Corvettes. Find the predicted sales price of varlet Smiths 4-year-old Corvette. Determine a 95% prediction interval for the sales price of varlet Smiths 4-year-old Corvette. Note that the following step are not required for all analysesonly put to death the necessary steps to complete your problem. Use the above steps as a guide to the correct SPSS steps. 1.Enter the age time value into one uncertain and the corr esponding sales price values into another multivariate (see figure, below). 2. study Graphs ? Legacy Dialogs ? Scatter/Dot (select Simple then click the touch on button) with the Y axis variable (Price) and the X Axis variable ( ripen) slip ined (see figures, below). crack Titles to submit a descriptive title for your chartical record, and click hold out. tittle-tattle OK. Your output should look similar to the figure below. a. Graph the data in a scatterplot to determine if there is a possible linear relationship. The points seem to follow a somewhat linear pattern with a negative slope. . Select Analyze ? Correlate ? Bivariate (see figure, below). 4. Select Age and Price as the variables, select Pearson as the correlation coefficient, and click OK (see the left figure, below). b. Compute and interpret the linear correlation coefficient, r. The correlation coefficient is 0. 9679 (see the pay off figure, above). This value of r suggests a strong negative linear correlati on since the value is negative and penny-pinching to 1. Since the above value of r suggests a strong negative linear correlation, the data points should be clustered well about a negatively sloping regression line.This is consistent with the graph obtained above. on that pointfore, since we see a strong negative linear relationship mingled with Age and Price, linear regression analysis can continue. 5. Since we eventually motivation to predict the price of 4-year-old Corvettes (parts jm), enter the number 4 in the Age variable column of the data window after the last row. Enter a . for the corresponding Price variable value (this lets SPSS cope that we want a prediction for this value and not to include the value in any other computations) (see left figure, below). . Select Analyze ? Regression ? Linear (see responsibility figure, above). 7. Select Price as the dependent variable and Age as the independent variable (see upperleft figure, below). Click Statistics, select Esti mates and effrontery Intervals for the regression coefficients, select Model fit to obtain r2, and click dwell (see upper-right figure, below). Click Plots, select Normal Probability Plot of the reliefs, and click take place (see lower-left figure, below).Click Save, select Unstandardized predicted values, select Unstandardized and Studentized residuals, select Mean (to obtain a confidence intervaloutput in the Data Window) and Individual (to obtain a prediction intervaloutput in the Data Window) at the 95% level (or whatever level the problem requires), and click Continue (see lower-right figure, below). Click OK. The output from this procedure is extensive and will be shown in parts in the following answers. c. Determine the regression equation for the data. From above, the regression equation is Price = 29160. 1942 (2790. 2913)(Age). 8.From within the output window, double-click on the scatterplot to enter Chart Editor mode. From the Elements menu, select Fit Line at thorou ghgoing. Click the shut out box. Now your scatterplot displays the linear regression line computed above. Graph the regression equation and the data points. d. e. Identify outliers and potential influential observations. There do not appear to be any points that lie furthest from the cluster of data points or far from the regression line thusly there are no possible outliers or influential observations. f. Compute and interpret the coefficient of determination, r2. The coefficient of determination is 0. 368 therefore, about 93. 68% of the variation in the price data is explained by age. The regression equation appears to be very serviceable for making predictions since the value of r 2 is close to 1. 9. The residuals and standardized values (as well as the predicted values, the confidence interval endpoints, and the prediction interval endpoints) can be found in the data window. 10. To create a residual plot, select Graphs ? Legacy Dialogs ? Scatter/Dot (Simple) with the residua ls (RES_1) as the Y Axis variable and Age as the X Axis variable. Click Titles to enter relaxation Plot as the title for your graph, and click Continue.Click OK. Double-click the resulting graph in the output window, select Options ? Y Axis university extension Line, select the Reference Line tab in the properties window, attention deficit hyperactivity disorder space of line 0, and click Apply. Click the close box to exit the chart editor (see left plot, below). 11. To create a studentized residual plot (what the textbook calls a standardized residual plot), select Graphs ? Legacy Dialogs ? Scatter/Dot (Simple) with the studentized residuals (SRES_1) as the Y Axis variable and Age as the X Axis variable. Click Titles to enter Studentized Residual Plot as the title for your graph, and click Continue.Click OK. Double-click the resulting graph in the output window, select Options ? Y Axis Reference Line, select the Reference Line tab in the properties window, add position of line 0, and click Apply. If 2 and/or -2 are in the range covered by the y-axis, absorb the last steps to add a reference line at 2 and -2 (see right plot, above) any points that are not between these lines are considered potential outliers. If 3 and/or -3 are in the range covered by the y-axis, repeat the last steps to add a reference line at 3 and -3 any points that are beyond these lines are considered outliers. 2. To assess the due north of the residuals, consult the P-P Plot from the regression output. g. Obtain the residuals and create a residual plot. Decide whether it is reasonable to consider that the assumptions for regression analysis are met by the variables in questions. The residual plot shows a random scatter of the points (independence) with a constant spread (constant variance). The studentized residual plot shows a random scatter of the points (independence) with a constant spread (constant variance) with no values beyond the 2 standard deviation reference lines (no ou tliers).The normal probability plot of the residuals shows the points close to a diagonal line therefore, the residuals appear to be approximately commonly distributed. Thus, the assumptions for regression analysis appear to be met. h. At the 10% consequence level, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and, hence, that age is useful as a soothsayer of sales price for Corvettes? smell 1 Hypotheses H 0 = 0 (Age is not a useful predictor of price. ) H a 0 (Age is a useful predictor of price. ) beat 2 Step 3 Step 4 Significance direct 0. 05 Critical Value(s) and Rejection Region(s) Reject the null hypothesis if p-value ? 0. 05. Test Statistic (choose either the T-test mode or the F-test methodnot both) T = 10. 8873, and p-value = 0. 00000448 Step 5 Step 6 F = 118. 5330, and p-value = 0. 00000448 Conclusion Since p-value = 0. 00000448 ? 0. 05, we shall reject the null hypothesis. State end in words At t he = 0. 05 level of significance, there exists enough evidence to conclude that the slope of the population regression line is not zippo and, hence, that age is useful as a predictor of price for Corvettes. . Obtain and interpret a 95% confidence interval for the slope, ? , of the population regression line that relates age to sales price for Corvettes. We are 95% overconfident that the slope of the true regression line is somewhere between 3381. 2946 and 2199. 2880. In other words, we are 95% confident that for every year sure-enough(a) Corvettes get, their average price decreases somewhere between $3,381. 2946 and $2,199. 2880. j. Obtain a point estimate for the mean sales price of all 4-year-old Corvettes. The point estimate (PRE_1) is 17999. 0291 dollars ($17,999. 0291). k.Determine a 95% confidence interval for the mean sales price of all 4-year-old Corvettes. We are 95% confident that the mean sales price of all four-year-old Corvettes is somewhere between $16,958. 4604 (L MCI_1) and $19,039. 5978 (UMCI_1). l. Find the predicted sales price of jak Smiths selected 4-year-old Corvette. The predicted sales price is 17999. 0291 dollars ($17,999. 0291). m. Determine a 95% prediction interval for the sales price of Jack Smiths 4-year-old Corvette. We are 95% certain that the individual sales price of Jack Smith? s Corvette will be somewhere between $14,552. 9173 (LICI_1) and $21,445. 1410 (UICI_1).