Question

Homework 4 Use the hand span data that we collected in class for homework Suppose you want to buy someone a pair of love, but you do not know their love size. Usually, we do have a pretty good idea of the person's height. Let' asume that the right hand span is a rood indicator of the love size. So let find the best predictor of right hand span be on the person's height. Once we can predict the right hand span, we can make a better educated guess in choosing the glove size for the gift. for both gendersyeded for males and fem A. Visualizing the Relationship Between Right Hand Span and Height 1. Use Minitab to draw a scatterplot of the data setting Xheight and Y right hand span. Label the points with the gender of the person that provided the data point. ii. Describe the general association between the variables. Describe the general shape of the relationship between the explanatory variable (height) and the response variable (right hand span). Be sure to mention whether the relationship is linear. If the relationship between the variables is linear, then describe the direction (positive or negative slope), and the strength of the linear sciation. Are there any outliers? iii. Guess the position of the regression line. Without any numerical calculations, use a ruler to trace a dashed line that in your judgement best captures the linear trend in the relationship between X and Y in the scatterplot (there is no right or wrong answer). In your opinion, is a separate line needed for males and females, or does a single line describe the relationship between X and Y for both genders? iv. Now find the equation ý = a + br that describes the line that you sketched on the scatterplot. Remember that two points are needed to determine the equation of a line. So, select two points on the line that you sketched and take great care to accurately record the (X,Y) coordinates. The two points just selected are not necessarily data points, they are just two points that fall on the line! Proceed to compute the equation of the line that passes through these two points. B. Least Squares Regression for Predicting Right Hand Span from Height i. Compute the least squares regression line. Using Minitab, compute the least squares regression line for predicting Y (right hand span) using the explanatory variable X (height). a. Write down the least squares regression equation for predicting Y (right hand span) using the explanatory variable X (height). b. Give an interpretation of the value of the slope within the context of the problem. Does it make sense? c. Give an interpretation of the value of the intercept within the context of the problem. Does it make sense? d. Give the value, and an interpretation of R2 (the coefficient of determination). e. Use Least Squares Regression for Predicting right Hand Span from height: If your friend's height is 16 cm, calculate your friend's right hand span in centimeter? ii. Understanding the Regression Effect sketch the regression line in a manner that illustrates the concept of "regression towards the mean"(x-height and Y = right hand span). C. Online assignments on sapling.

DATA:

Right hand span	Left Hand Span	height	gender
19	19.5	170.18	F
17.5	17.5	152.94	F
19	19	149.86	F
20	21	154.94	F
23	23	177.8	M
21	22	177.8	M
23	23.2	180.34	M
23	22.5	187.96	M
22	22.7	167.6	M
22.3	21.7	177.8	M
21	21	157.4	F
22.5	24	175.3	M
25	25.5	188	M
20.5	20.7	164	F
19.9	20.1	165.1	F
21.5	21.5	160	F
19.5	19.5	152	F
21	21	167	F
19	19	160	F
21	20.5	154.9	F
22	21	170.18	M
21.7	21.7	177.8	M
19	19	154.94	F
18.1	18.1	162.56	F
20.3	20.3	157.48	F
22.7	22.7	182.88	M

Answer 1

a. Write down the least squares regression equation for predicting Y (right hand span) using the explanatory variable X (height).

The least-squares regression equation is:

Y = 0.4368 + 0.1227*X

b. Give an interpretation of the value of the slope within the context of the problem. Does it make sense?

When height is increased by 1, right-hand span will increase by 0.1227.

c. Give an interpretation of the value of the intercept within the context of the problem. Does it make sense?

When height is 0, right-hand span will increase by 0.4368. It does not make sense because height cannot be 0.

d. Give the value, and an interpretation of R2 (the coefficient of determination).

The coefficient of determination is 0.632. It means that 63.2% of the variability in Y is explained by X.

The regression output is:

	r²	0.632
	r	0.795
	Std. Error	1.103
	n	26
	k	1
	Dep. Var.	Right hand span
ANOVA table
Source	SS	df	MS	F	p-value
Regression	50.1334	1	50.1334	41.19	1.23E-06
Residual	29.2101	24	1.2171
Total	79.3435	25
Regression output					confidence interval
variables	coefficients	std. error	t (df=24)	p-value	95% lower	95% upper
Intercept	0.4368
height	0.1227	0.0191	6.418	1.23E-06	0.0832	0.1621

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