Question

Question 1 50/2 pts 5399 Details Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = 9 Xy 4 6.92 5 6.21 6 10 7 7.39 8 6.18 8.17 10 7.96 9.75 12 6.84 13 6.93 14 7.32 15 6.81 16 9.5

Answer 1

Solution :

Let X = Years

Y = Heigh Tempreture

Regression equation is;

Where b1 and b0 are the slope and intecept parameter respectively

$b_{1} = \frac{\sum(x - \bar{x})(y - \bar{y})}{\sum(x -\bar{x})^2}$

$b_{0} = \bar{y} - b_{1}*\bar{x}$

regression equation is;

By using excel calculation :

Data < Tool analysis(Regression) (Ok) < ( select input X range , Input y range ,label tick , and output range (ok)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.15183868
R Square	0.023054985
Adjusted R Square	-0.065758199
Standard Error	1.350108221
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.473178	0.473178	0.25959	0.620468
Residual	11	20.05071	1.822792
Total	12	20.52389
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	7.180879121	1.068527	6.720356	3.29E-05	4.829068	9.53269	4.829068	9.53269
X	0.050989011	0.100077	0.509499	0.620468	-0.16928	0.271256	-0.16928	0.271256

Book1 - Microsoft Excel Home Insert Page Layout Formulas Data Review View Clear Reapply Y Advanced Show Detail Data Analysis Hide Detail ? Solver From Access From Web Filter Connections ET Properties Refresh All Edit Links Connections Existing Connections % Sort From From Other Text Sources Get External Data Group Ungroup Subtotal Text to Remove Data Consolidate What if Columns Duplicates Validation Analysis Data Tools Sort & Filter Outline Analysis D23 (x fix A B с D E F H 1 J K L M N 0 1 X Y 2 4 6.92 3 6.21 5 6 4 10 5 7.39 7 8 6 6.18 7 9 8.17 8 10 7.96 SUMMARY OUTPUT 9 11 10 12 13 9.75 6.84 6.93 7.32 6.81 14 11 12 13 14 15 16 Regression Statistics Multiple R 0.15183868 R Square 0.023054985 Adjusted R Squa -0.065758199 Standard Error 1.350108221 Observations 13 15 16 9.5 17 ANOVA 18 df F ignificance F 0.25959 0.620468 19 20 21 22 Regression Residual Total SS MS 1 0.473178 0.473178 11 20.05071 1.822792 12 20.52389 23 24 Intercept х Coefficients andard Erri t Stat P-value Lower 95%Upper 95%ower 95.0%pper 95.0% 7.180879121 1.068527 6.720356 3.29E-05 4.829068 9.53269 4.829068 9.53269 0.050989011 0.100077 0.509499 0.620468 -0.16928 0.271256 -0.16928 0.271256 25 26 27 28 29 30 31 K Sheet1 Sheet2 Sheet3