Question

9. Find the regression​ equation, letting overhead width be the predictor​ (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 2.3 cm. Can the prediction be​ correct? What is wrong with predicting the weight in this​ case? Use a significance level of 0.05.

Overhead_Width_(cm)    Weight_(kg)

7.8         157

7.4         171

9.6         258

8.2         173

7.2         151

7.6         174

What is the regression​ equation?

Ŷ=____+____x

(Round to two decimal places as​ needed.)

The best predicted weight for an overhead width of 2.3 cm is _____ kg.

​(Round to one decimal place as​ needed.)

Can the prediction be​ correct? What is wrong with predicting the weight in this​ case?

A.The prediction cannot be correct because a negative weight does not make sense. The regression does not appear to be useful for making predictions.

B.The prediction cannot be correct because there is not sufficient evidence of a linear correlation. The width in this case is beyond the scope of the available sample data.

C.The prediction cannot be correct because a negative weight does not make sense. The width in this case is beyond the scope of the available sample data.

D.The prediction can be correct. There is nothing wrong with predicting the weight in this case.

Answer 1

We get regression output using excel as :

Data tab > data analysis > regression . Insert ranges of y and x values.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.936158
R Square	0.876392
Adjusted R Square	0.84549
Standard Error	15.34246
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6675.769	6675.769	28.36034	0.005984
Residual	4	941.5641	235.391
Total	5	7617.333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-153.541	63.06864	-2.43451	0.071631	-328.648	21.56532
Overhead width	41.95079	7.877428	5.325442	0.005984	20.07954	63.82204

From output we get : slope = b= 41.95 , intercept = a =-153.54

Hence the estimated regression equation is,

We have overhead width = x = 2.3

= -57.06

So we get best predicted weight = -57.06 kg.

The correct option is,

A.The prediction cannot be correct because a negative weight does not make sense. The regression does not appear to be useful for making predictions.