Question

Use the dependent variable (labeled Y) and one of the independent variables (labeled X1, X2, and X3) in the data file. Select and use one independent variable throughout this analysis. Use Excel to perform the regression and correlation analysis to answer the following.

Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the "best fit" line. Interpret.

Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.

Determine the coefficient of correlation. Interpret.

Determine the coefficient of determination. Interpret.

Test the utility of this regression model, represented by a hypothesis test of b=0 using α=0.10. Interpret results, including the p-value.

Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable?

Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.

Compute the 99% confidence interval for the dependent variable, for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use same value in the next step). Interpret this interval.

Using the same chosen value for part (8), estimate the 99% prediction interval for the dependent variable. Interpret this interval.

What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.

Sales (Y)	Calls (X1)	Time (X2)	Years (X3)	Type
40	144	17.4	0.00	NONE
46	145	16.8	0.00	ONLINE
37	152	19.8	0.00	NONE
47	164	15.3	0.00	ONLINE
42	135	16.1	0.00	NONE
44	169	8.9	0.00	ONLINE
52	173	18.6	0.00	ONLINE
53	184	15.2	0.00	ONLINE
49	152	22.3	0.00	ONLINE
49	166	16.2	0.00	ONLINE
45	185	13.3	1.00	ONLINE
47	157	14.3	1.00	GROUP
42	148	16.9	1.00	NONE
43	131	18.5	1.00	NONE
44	150	18.4	1.00	NONE
43	148	15.9	1.00	ONLINE
55	189	12	1.00	ONLINE
49	188	20.4	1.00	NONE
51	190	11.3	1.00	ONLINE
37	137	18.1	1.00	ONLINE
51	167	16.2	1.00	ONLINE
37	130	15.6	1.00	GROUP
37	142	18.5	1.00	NONE
46	153	14.1	1.00	ONLINE
39	149	18.8	1.00	GROUP
46	151	16	1.00	GROUP
45	158	13.9	1.00	ONLINE
46	172	12.5	1.00	ONLINE
47	188	16.3	1.00	NONE
37	148	16.2	1.00	GROUP
46	162	12.1	1.00	GROUP
52	177	14.5	1.00	ONLINE
48	175	13.7	1.00	ONLINE
40	150	10.8	1.00	GROUP
53	182	10.5	1.00	ONLINE
54	197	11.8	1.00	ONLINE
46	148	13.1	1.00	GROUP
41	153	14.7	1.00	GROUP
44	169	13.6	1.00	ONLINE
47	176	14.1	2.00	ONLINE
47	183	12.8	2.00	ONLINE
48	136	14.1	2.00	ONLINE
52	197	13.9	2.00	ONLINE
37	120	12	2.00	NONE
49	184	16.7	2.00	ONLINE
43	173	19.8	2.00	ONLINE
42	153	15.5	2.00	GROUP
37	133	19.8	2.00	NONE
42	154	14.8	2.00	ONLINE
53	178	13.2	2.00	ONLINE
45	138	18.9	2.00	NONE
42	167	18	2.00	NONE
48	171	13	2.00	GROUP
46	162	16.2	2.00	ONLINE
49	149	21.1	2.00	GROUP
48	174	18.6	2.00	GROUP
45	173	17.6	2.00	ONLINE
45	155	18.9	2.00	GROUP
44	159	18.1	2.00	ONLINE
54	174	10.8	2.00	NONE
44	139	15.2	2.00	NONE
41	158	19.3	2.00	ONLINE
43	145	18.6	2.00	NONE
47	193	13.5	2.00	ONLINE
38	145	17.1	2.00	NONE
50	184	15.6	2.00	ONLINE
41	128	15.5	2.00	NONE
45	177	14.2	2.00	GROUP
49	170	16.1	3.00	NONE
38	122	19.3	3.00	GROUP
46	171	13.6	3.00	GROUP
37	148	15.7	3.00	GROUP
42	167	17.7	3.00	ONLINE
44	148	13.5	3.00	GROUP
45	164	16.7	3.00	NONE
45	146	12	3.00	GROUP
48	177	13.9	3.00	ONLINE
49	160	13.6	3.00	GROUP
46	149	17.8	3.00	NONE
45	140	11	3.00	GROUP
45	130	20.6	3.00	GROUP
43	166	17.6	3.00	ONLINE
44	188	12.9	3.00	GROUP
41	157	11.5	3.00	ONLINE
41	155	13.6	3.00	GROUP
43	153	15.2	3.00	GROUP
37	145	18	3.00	NONE
34	133	15.2	4.00	GROUP
51	177	11.4	4.00	NONE
43	169	13.3	4.00	NONE
39	156	13.3	4.00	NONE
40	125	12.2	5.00	NONE
44	182	15.5	5.00	NONE
48	156	15.1	4.00	ONLINE
43	148	14.5	4.00	ONLINE
39	138	17.7	4.00	GROUP
42	160	10.6	4.00	NONE
54	180	11.8	5.00	GROUP
51	167	12.6	6.00	ONLINE
48	165	19.8	6.00	ONLINE

Answer 1

I have used X1 as independent variable

using excel for linear regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.693202078
R Square	0.480529122
Adjusted R Square	0.475228398
Standard Error	3.428879729
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1065.832813	1065.832813	90.65350123	1.3252E-15
Residual	98	1152.207187	11.7572162
Total	99	2218.04
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	16.07981771	3.042128936	5.285712095	7.59202E-07	10.04281185	22.11682358	8.088354613	24.07128081
Calls (X1)	0.180236613	0.018930005	9.521213223	1.3252E-15	0.142670634	0.217802591	0.130508794	0.229964431

Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.

y^ = 16.0798+ 0.1802 * x

Determine the coefficient of correlation. Interpret.
r = 0.6932
this mean there is positive correlation between two variable
the strength is moderate

Determine the coefficient of determination. Interpret.
this is given by R^2 = 0.4805
this means that this model explains 48.05 % of variation in y

Test the utility of this regression model, represented by a hypothesis test of b=0 using α=0.10. Interpret results, including the p-value.

p-value for b is 1.3252*10^(-15) << 0.10
hence we reject the null hypothesis
the model is useful

Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable?
The model is significant
although R^2 is less , maybe we can use other independent variable to predict more accurately

Compute the confidence interval for b, using a 95% confidence level. Interpret this interval

95% confidence interval for b1 (0.1427,0.2178)

Please post questions again

I have solved more than 4 sub-parts which i was supposed to do

Please g