Question

Consider the following set of dependent and independent variables. Complete parts a through c below. y 10 11 14 14 20 24 26 32 저15597121521 x2 17 11 13 11 2 8 6 4 a. Using technology, construct a regression model using both independent variables. y = 1 3.5734 ) + ( 0.9496 ) x 1 + (-0.4001 ) x2 (Round to four decimal places as needed.) b. Test the significance of each independent variable using a 0.10. Test the significance of x1. Identify the null and alternative hypotheses. 0. P1 Type integers or decimals.) Calculate the appropriate test statistic. The test statistic is (Round to two decimal places as needed.) The critical value(s) is/are) Round to two decimal places as needed. Use a comma to separate answers as needed.) State the conclusion for the test of significance for x1 the null hypothesis. There is evidence to conclude that there a relationship between x1 and y. Test the significance of x2 Identify the null and alternative hypotheses. Type integers or decimals.) Calculate the appropriate test statistic. The test statistic is The critical value(s) is(are) Round to two decimal places as needed. Use a comma to separate answers as needed.) State the conclusion for the test of significance for x2 ▼ the null hypothesis There is evidence to conclude that therea relationship between x2 and y c. Interpret the p-value for each independent variable nterpret the p-value for the hypothesis test corresponding to x1 anda0.0 ince p-valueis the null hypothesis. There is ' evidence to conclude that there | ▼| a relationship between x1 and y Round to three decimal places as needed.) Interpret the p-value for the hypothesis test corresponding to x2 and 010 9the nul hypothesis There Sincepeak"-Dis the null hypothesis. There is evidence to conclude that therea relationship between x2 and y Enter your answer in each of the answer boxes.

Answer 1

using excel data analysis tool for regression, following o/p is obtained

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.960496
R Square	0.922553
Adjusted R Square	0.891574
Standard Error	2.607284
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	404.8854	202.4427	29.78005	0.001669
Residual	5	33.98965	6.79793
Total	7	438.875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	13.57335	4.251581	3.192543	0.024196	2.644317	24.50239	2.644317	24.50239
X1	0.949587	0.214177	4.433665	0.006805	0.399029	1.500145	0.399029	1.500145
X2	-0.40008	0.277083	-1.44391	0.208369	-1.11235	0.312183	-1.11235	0.312183

b)              
the test statictic = 4.43              
              
α=0.10              
df=N-1 = 7              
critical value= -1.89 and +1.89              
              
since, test stat > critical value = 1.89, reject Ho              
              
reject the null hypothesis, there is enough evidence to conclude that there is a relationship between x1 and y              
              
              
              
H0: ß2 = 0              
H1: ß2 ╪0              
              
test stat = -1.44              
              
critical value= -1.89 and +1.89              
do not reject the null hypothesis, there is not enough evidence to conclude that there is a relationship between x2 and y              
              
c) for x1              
since, p-value=0.007 is less than α, reject the null hypothesis.              
there is enough evidence to conclude that there is a relationship between x1 and y              
              
for x2              
since, p-value=0.208 is greater than α,do not reject the null hypothesis.              
there is not enough evidence to conclude that there is a relationship between x1 and y