Question

Question #2 - Review 'Cars Database'. From this data set develop the following: a. One bivariate regression b. One multiple regression c. Provide an effective chart displaying each of the two regressions. Charts should be presentation ready with effective title and labels. d. Provide a brief description of each of the two regressions (please use a text box in your Excel spreadsheet for your descriptions). Also, be sure to correctly identify and describe your independent and dependent variables, linear equation (answer), R, R square, F statistics, t statistic, other.

ENGINE	HORSE	WEIGHT	ACCEL	YEAR	CYLINDER	MPG
307	130	3504	12	70	8	18
350	165	3693	12	70	8	15
318	150	3436	11	70	8	18
304	150	3433	12	70	8	16
302	140	3449	11	70	8	17
429	198	4341	10	70	8	15
454	220	4354	9	70	8	14
440	215	4312	9	70	8	14
455	225	4425	10	70	8	14
390	190	3850	9	70	8	15
383	170	3563	10	70	8	15
340	160	3609	8	70	8	14
400	150	3761	10	70	8	15
455	225	3086	10	70	8	14
113	95	2372	15	70	4	24
198	95	2833	16	70	6	22
199	97	2774	16	70	6	18
200	85	2587	16	70	6	21
97	88	2130	15	70	4	27
97	46	1835	21	70	4	26
110	87	2672	18	70	4	25
107	90	2430	15	70	4	24
104	95	2375	18	70	4	25
121	113	2234	13	70	4	26
199	90	2648	15	70	6	21
360	215	4615	14	70	8	10
307	200	4376	15	70	8	10
318	210	4382	14	70	8	11
97	88	2130	15	71	4	27
140	90	2264	16	71	4	28
113	95	2228	14	71	4	25
232	100	2634	13	71	6	19
225	105	3439	16	71	6	16
250	100	3329	16	71	6	17
250	88	3302	16	71	6	19
232	100	3288	16	71	6	18
350	165	4209	12	71	8	14
400	175	4464	12	71	8	14
351	153	4154	14	71	8	14
318	150	4096	13	71	8	14
383	180	4955	12	71	8	12
400	170	4746	12	71	8	13
400	175	5140	12	71	8	13
258	110	2962	14	71	6	18
140	72	2408	19	71	4	22
250	100	3282	15	71	6	19
250	88	3139	15	71	6	18
122	86	2220	14	71	4	23
116	90	2123	14	71	4	28
79	70	2074	20	71	4	30
88	76	2065	15	71	4	30
71	65	1773	19	71	4	31
72	69	1613	18	71	4	35
97	60	1834	19	71	4	27
91	70	1955	21	71	4	26
113	95	2278	16	72	4	24
98	80	2126	17	72	4	25
97	54	2254	24	72	4	23
140	90	2408	20	72	4	20
122	86	2226	17	72	4	21
350	165	4274	12	72	8	13
400	175	4385	12	72	8	14
318	150	4135	14	72	8	15
351	153	4129	13	72	8	14

Answer 1

Here Depenedent variable is MPG and independent variable all except MPG a) bivariate regression here dependent variable is MPG and independent variable x1 is ENGINE and x2 HORSE Data Analysis > regression> column 1 is y choose MPG and column 2 is ENGINE AND HORSE DATA SUMMARY OUTPUT ANOVA Regression Statistics Multiple R df gnificance F MS 0.899392 SS R Square 0.808905 Regressio 2 1779.276 889.6378 129.1067 1.2E-22 yhat is estimated equation Adjusted R Squa Residual 0.80264 61 420.3337 6.890717 Standard Error 2.625018 Total 63 2199.609 yhat 30.08546-0.04007*x1-0.00705*x2 Observations 64 Coefficientsandard Err P-value Lower 95%Upper 95%ower 95.0pper 95.0% t Stat Intercept 30.08546 0.948233 31.72791 1.27E-39 28.18935 31.98157 28.18935 31.98157 ENGINE -0.04007 0.006671 -6.00597 1.14E-07 -0.05341 -0.02673 -0.05341 -0.02673 HORSE -0.00705 0.016761 -0.42037 0.675695 0.04056 0.02647 0.04056 0.02647 R square value is 0.808905 it is very good F statistics is 129.1067 and p value is 0.000 here we accept H1 that is given regression model is significant model

b) bivariate regression here dependent variable is MPG and independent variable all except MPG regression> column 1 is y choose MPG and column 2 is ENGINE to Cylinder DATA Data Analysis SUMMARY OUTPUT ANOVA Regression Statistics df Multiple R 0.936836 gnificance F SS MS F R Square 0.877662 Regressio 6 1930.514 321.7523 68.15383 3.46E-24 Adjusted R Squa 0.864785 Residual 57 269.0954 4.720972 Standard Error Total 63 2199.609 2.17278 Observations F statistics is 68.15383 64 p value is 0.00 Coefficientandard Err P-value Lower 95%Upper 95%ower 95.0pper 95.0% t Stat Intercept 50.1493 32.07824 1.563343 0.123507 -14.0863 114.3849 -14.0863 114.3849 here p value is less than ENGINE -0,01223 0.010058 -1.21631 0.22888 -0.03237 0.007907 -0.03237 0.007907 alpha value hence here regression HORSE -0.00667 0.015729 -0.42416 0.673046 0.03817 0.024825 -0.03817 0.024825 model is significant model WEIGHT -0.00276 0.000886 3.12049 0.002833 -0.00454 -0.00099 -0.00454 -0.00099 ACCEL -0.2774 0.157223 -1,76439 0.083024 -0.59224 0.037431 -0.59224 0.037431 EA .10962 .4 0 2 0.810401 0. 801106 CYLINDER -1.04308 0.574162 -1,81671 0.074521 -2.19282 0.106656-2.19282 0.106656 yhat-50.1493-0.01223*x1-0.00667*x2-0.00276*x3-0.2774*x4-0.10962*x5-1.04308*x6

Normal Probability Plot 35 30 25 20 15 10 0 0 20 40 60 80 100 120 Sample Percentile from normal probability plot here we line is linear hence it is good model for multiple regression model MPG 4 8 9un o

d) SUMMARY OUTPUT ANOVA Regression Statistics gnificance F Multiple R df 0.899392 SS MS F R Square 0.808905 Regressio 2 1779.276 889.6378 129.1067 1.2E-22 yhat is estimated equation Adjusted R Squa Residual 0.80264 61 420.3337 6.890717 Standard Error Total 2.625018 63 2199.609 yhat 30.08546-0.04007*x1-0.00705*x2 Observations 64 Coefficientsandard Err P-value Lower 95%Upper 95%ower 95.0pper 95.0% t Stat Intercept 30.08546 0.948233 31.72791 1.27E-39 28.18935 31.98157 28.18935 31.98157 ENGINE -0.04007 0.006671 -6.00597 1.14E-07 -0.05341 -0.02673 -0.05341 -0.02673 HORSE -0.00705 0.016761 -0.42037 0.675695 -0.04056 0.02647 -0.04056 0.02647 R square value is 0.808905 it is very good F statistics is 129.1067 and p value is 0.000 here we accept H1 that is given regression model is significant model.

multivariate regression here dependent variable is MPG and independent variable all except MPG DATA Data Analysis > regression> column 1 is y choose MPG and column 2 is ENGINE to Cylinder SUMMARY OUTPUT Regression Statistics Multiple R 0.936836 R Square 0.877662 Adjusted R Squa 0.864785 Standard Error 2.17278 E statistics is 68.15383 Observations 64 p value is 0.00 ANOVA df gnificance F SS MS F here p value is less than Regression 6 1930.514 321.7523 68.15383 3.46E-24 alpha value hence here regression Residual 57 269.0954 4.720972 model is significant model Total 63 2199.609 yhat-50.1493-0.01223*x1-0.00667*x2-0.00276*x3-0.2774*x4-0.10962*x5-1.04308*x6