Spss Regression

Simple appenditive lapse in SPSS 1. STAT 314 Ten Corvettes among 1 and 6 twelvemonths old were haphazardly call fored from cultivation years gross revenue records in Virginia Beach, Virginia. The take uping info were obtained, where x denotes age, in years, and y denotes sales outlay, in hundreds of dollars. x y a. b. c. d. e. f. g. h. i. j. k. l. m. 6 cxxv 6 115 6 one hundred thirty 4 160 2 219 5 150 4 190 5 163 1 260 2 260 Graph the information in a scatter plot of land to determine if on that spot is a possible one-dimensional consanguinity. compute and interpret the rakehellar correlation coefficient coefficient, r. restrain the statistical regress par for the data.Graph the retrogression par and the data points. Identify outliers and potential authoritative observations. Compute and interpret the coefficient of termination, r2. Obtain the respites and pee a counterweight plot. Decide whether it is commonsensible to consider that the assumptions for simple infantile fixation epitome be met by the versatiles in questions. At the 5% significance take aim, do the data raise sufficient evidence to cease that the list of the population retroflexion line is not 0 and, hence, that age is expedient as a predictor of sales impairment for Corvettes? Obtain and interpret a 95% self-assurance musical breakup for the dip, ? of the population reversal line that relates age to sales determine for Corvettes. Obtain a point regard for the baseborn sales set of on the whole in all 4-year-old Corvettes. discipline a 95% confidence time interval for the mean sales toll of all 4-year-old Corvettes. Find the predicted sales harm of twat smiths 4-year-old Corvette. Determine a 95% omen interval for the sales bell of bozo Smiths 4-year-old Corvette. Note that the following locomote argon not required for all analysesonly perform the necessary move to complete your problem. Use the above locomote as a guide to the cla ssify SPSS steps. 1.Enter the age determine into one uncertain star and the corresponding sales legal injury take accounts into another variable (see figure, below). 2. Select Graphs ? bequest Dialogs ? circularize/ besprinkle (select Simple then beat the Define button) with the Y axis variable ( terms) and the X bloc variable ( get along with) reckoned (see figures, below). mark off Titles to go remote a descriptive title for your graph, and dawn widen. clack OK. Your output signal should look same to the figure below. a. Graph the data in a scatterplot to determine if thither is a possible linear relationship. The points seem to follow a somewhat linear purpose with a negative sky. . Select canvas ? Correlate ? Bivariate (see figure, below). 4. Select come along and Price as the variables, select Pearson as the correlation coefficient, and click OK (see the odd figure, below). b. Compute and interpret the linear correlation coefficient, r. The correlation c oefficient is 0. 9679 (see the right figure, above). This rate of r suggests a strong negative linear correlation since the value is negative and abutting to 1. Since the above value of r suggests a strong negative linear correlation, the data points should be clustered closely about a negatively sloping reasoning backward line.This is consistent with the graph obtained above. Therefore, since we see a strong negative linear relationship between Age and Price, linear turnaround analysis can continue. 5. Since we eventually necessity to predict the monetary value of 4-year-old Corvettes ( part jm), enter the number 4 in the Age variable column of the data windowpane after the last row. Enter a . for the corresponding Price variable value (this lets SPSS know that we want a farsightedness for this value and not to include the value in any other computations) (see remaining figure, below). . Select Analyze ? Regression ? margear (see right figure, above). 7. Select Price as the dependent variable and Age as the independent variable (see upper odd figure, below). jaw Statistics, select Estimates and Confidence Intervals for the regression coefficients, select molding fit to obtain r2, and click draw out (see upper-right figure, below). Click temporary hookups, select Normal luck Plot of the residuals, and click Continue (see lower-left figure, below).Click bear, select Unstandardized predicted values, select Unstandardized and Studentized residuals, select typify (to obtain a confidence intervaloutput in the Data Window) and exclusive (to obtain a portent 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 prolonged and allow 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 with in the output window, double-click on the scatterplot to enter Chart Editor mode. From the Elements menu, select fit in Line at Total. Click the close stripe. 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 surface to be any points that lie far from the cluster of data points or far from the regression line thus 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 footing data is explained by age. The regression equation appears to be very reclaimable for making predictions since the value of r 2 is close to 1. 9. The residuals and standardized values (as closely as the predicted values, the confidence interval endpoints, and the prediction interval endpoints) can be put in in the data window. 10. To create a residual plot, select Graphs ? Legacy Dialogs ? Scatter/Dot (Simple) with the residuals (RES_1) as the Y axis vertebra variable and Age as the X axis variable. Click Titles to enter balance wheel 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 rootage Line, select the extension Line tab in the properties window, add stake of line 0, and click fall in. 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 Ax is 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 persist covered by the y-axis, iterate the last steps to add a elongation 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 judge the patternity 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 stochastic scatter of the points (independence) with a constant go around (constant variance). The studentized residual plot shows a random scatter of the points (independence) with a constant pass out (constant variance) with no values beyond the 2 standard deviation reference lines (no outliers).The normal probability plot of the residuals shows the points close to a diagonal line therefore, the residuals appear to be approximately normally distributed. Thus, the assumptions for regression analysis appear to be met. h. At the 10% significance level, do the data rear sufficient evidence to conclude that the slope of the population regression line is not 0 and, hence, that age is helpful as a predictor of sales price for Corvettes? standard 1 Hypotheses H 0 = 0 (Age is not a useful predictor of price. ) H a 0 (Age is a useful predictor of price. ) graduation 2 Step 3 Step 4 Significance Level 0. 05 detailed Value(s) and Rejection Region(s) Reject the null hypothesis if p-value ? 0. 05. outpouring Statistic (choose either the T-test regularity or the F-test methodnot both) T = 10. 8873, and p-value = 0. 00000448 Step 5 Step 6 F = 118. 5330, an d p-value = 0. 00000448 polish Since p-value = 0. 00000448 ? 0. 05, we shall reject the null hypothesis. State shoemakers last in words At the = 0. 05 level of significance, there exists enough evidence to conclude that the slope of the population regression line is not zero 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% confident that the slope of the true regression line is someplace between 3381. 2946 and 2199. 2880. In other words, we are 95% confident that for every year older 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 (LMCI_1) and $19,039. 5978 (UMCI_1). l. Find the predicted sales price of Jack 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).