Question

Heights​ (cm) and weights​ (kg) are measured for 100 randomly selected adult​ males, and range from heights of 139 to 192 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x overbarequals167.77 ​cm, y overbarequals81.54 ​kg, requals0.201​, ​P-valueequals0.045​, and ModifyingAbove y with caretequalsnegative 105plus1.04x. Find the best predicted value of ModifyingAbove y with caret ​(weight) given an adult male who is 158 cm tall. Use a 0.01 significance level.

Answer 1

The weight of an adult male who is 158 cm tall is 59.32 kg.

Explanation:

The regression equation representing the relationship between height and weight of a person is:

`\hat y=-105+1.04 x`

Here,

y = weight of a person (in kg)

x = height of a person (in cm)

The information provided is:

`\bar x=167.77\ \text{cm}\\\bar y=81.54\ \text{cm}\\r(X, Y)=0.201\\p-value=0.045`

The significance level of the test is, α = 0.01.

The hypothesis to test the significance of the correlation between height and weight is:

H₀: There is no relationship between the height and weight, i.e. ρ = 0.

Hₐ: There is a relationship between the height and weight, i.e. ρ ≠ 0.

Decision rule:

If the p-value of the test is less than the significance level, then the null hypothesis will be rejected and vice-versa.

According to information provided:

p-value = 0.045 > 0.01

The null hypothesis will not be rejected at 1% level of significance.

Thus, concluding that there is no relationship between the height and weight.

Compute the weight of an adult male with height, x = 158 cm as follows:

`\hat y=-105+1.04 x`

`=-105+(1.04* 158)\\=-105+164.32\\=59.32`

Thus, the weight of an adult male who is 158 cm tall is 59.32 kg.