Multiple Regression Lab

A collector of antique grandfather clocks sold at auction believes that the price received for the clocks depend on both the age of the clocks and the number of bidders at the auction. A sample of 32 auction prices of grandfather clocks along with their age and the number of bidders is given in the table below. Test the hypothesis that the mean auction price of a clock increases as the number of bidders increases and as the age of the Clock increases.

ID	Auction price	Age of clock	Number of bidders
1	1235	127	13
2	1080	115	12
3	845	127	7
4	1522	150	9
5	1047	156	6
6	1979	182	11
7	1822	156	12
8	1253	132	10
9	1297	137	9
10	946	117	9
11	1713	137	15
12	1024	113	11
13	1147	137	8
14	1092	153	6
15	1152	117	13
16	1336	126	10
17	2131	170	14
18	1550	182	8
19	1884	162	11
20	2041	184	10
21	845	143	6
22	1483	159	9
23	1055	108	14
24	1545	175	8
25	729	108	6
26	1792	179	9
27	1175	111	15
28	1593	187	8
29	785	111	7
30	744	115	7
31	1356	194	5
32	1262	168	7

1. What are the two independent variables?
2. What is the dependent variable?
3. State the null and the alternative hypothesis.
4. Open SPSS and create 4 variables. The first is the ID code for each Clock so that is a nominal scale. Then enter the three variables of interest in the study: auction price, age of the Clock, and number of bidders. Make sure that the auction price, age of the Clock, and number of bidders are both marked Scale under Measure.
5. Enter the data in the table above , and save when finished.
6. First create graphs to determine that the relationships between the variables. Use the same method that you used for the simple linear regression to create 3 scatter plots. One looking at the relationship between age and auction price; a second looking at the relationship between number of bidders an auction price; and a third looking at the relationship between age and number of bidders.
7. Report on your assessment of the graphs as to whether there are linear relationships between the variables.
8. You will run the regression the same way that you did when you analyzed the simple linear regression analysis. so click on regret analyze regret regression linear. Move the independent variables into the independent variables box and move the dependent variable into the dependent variable box.
9. Click on statistics and make sure the model fit box is checked and under regression coefficient, estimates is checked click OK.
10. Several tables of output appear supply the following information:
11. Under Model Summary, what is R Square?
12. What percentage of the variance in the data is explained by the regression line? (Hint: multiply R squared by 100 to turn it into a percentage.)
13. Under Coefficients, what is the Unstandardized Beta for the age variable?
14. Under Coefficients, what is the Unstandardized Beta for the number of bidders variable?
15. What is the t score for your age variable?
16. What is the t score for your number of bidders variable?
17. What is the p-value for the age variable? (it's under Sig. column)
18. What is the p-value for the number of bidders variable? (it's under Sig. column)
19. What is your conclusion (based on your p-value compared to alpha = .01) about the researchers' question about being able to predict the auction price from both the age of the clock and the number of bidders
20. Save the scatterplot and your output and submit with your paragraph explained below in k.

k. Write up the results. Here is a model. You can't just fill in the blanks. Type up a paragraph with your results. I have bolded what you need to insert and put them into parentheses. Do not put those in your written paper with the exception of ( = XXX, p = XXX). That does go in parentheses but don't bold.

A multiple regression was conducted to see if (INDEPENDENT VARIALBE1 AND INDEPENDENT VARIABLE2) predicted the (DEPENDENT VARIABLE). Using the enter method it was found that (INDEPENDENT VARIALBE1 AND INDEPENDENT VARIABLE2) explain a significant amount of the variance in the (DEPENDENT VARIABLE) (R SQUARED = .XX). The analysis shows that (INDEPENDENT VARIRABLE 1) significantly predicted value of (DEPENDENT VARIABLE) (Beta = X.XXX, t = XXXX, p = .XXX). In addition, the analysis shows that (INDEPENDENT VARIRABLE 2) significantly predicted value of (DEPENDENT VARIABLE) (Beta = X.XXX, t = XXXX, p = .XXX). Therefore, the null hypothesis is rejected, and the alternative is retained. / OR Therefore, the null hypothesis failed to be rejected, and it is retained. (CHOOSE OF THE TWO PREVIOUS SENTENCES, WHICHEVER IS CORRECT.). OR Therefore, the null hypothesis is rejected as it relates to (WHICHEVER INDEPENDENT VARIABLE IS SIGNIFICANT), we failed to be reject the null as it relates to WHICHEVER INDEPENDENT VARIABLE IS NOT SIGNIFICANT, and it is retained. (CHOOSE FROM THE THREE PREVIOUS SENTENCES, WHICHEVER IS CORRECT.)

Model results paragraph using different data.

A multiple regression was conducted to see if intelligence level and extroversion level predicted the total value of sales made by sales persons per week. Using the enter method it was found that intelligence and extroversion level explain a significant amount of the variance in the value of sales made per week (R² = .59). The analysis shows that intelligence level did not significantly predict value of sales per week (Beta = .23, t = 1.17, ns); however, extroversion level did significantly predict value of sales per week (Beta = .50, t = 2.53, p < .05). Therefore, the null hypothesis is rejected for extroversion but not for intelligence level.