Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 131131 to 191191 cm and weights of 3838 to 150150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x overbarxequals=167.90167.90 cm, y overbaryequals=81.4081.40 kg, requals=0.1080.108, P-valueequals=0.2850.285, and ModifyingAbove y with caretyequals=negative 107−107plus+1.181.18x. Find the best predicted value of ModifyingAbove y with carety (weight) given an adult male who is 185185 cm tall. Use a 0.050.05 significance level. The best predicted value of ModifyingAbove y with carety for an adult male who is 185185 cm tall is 111.3111.3 kg.

The best predicted value of weight for an adult male who is 185 cm tall is 111.5 kg.

Step-by-step explanation:

For this question, most of the heavy lifting has been done with the information provided in the question.

A regression analysis has been carried using the sample of 100 randomly selected adult males to find the correlation between the weight and height of the men.

x represents the height, which is then used to calculate y, the weight of the adult men.

The regression analysis yielded

x overbar x = 167.90 cm

y overbar y = 81.40 kg

r = 0.108

P-value = 0.285 and

Y = -107 + 1.181X

For an adult man with height 185 cm, X = 185, and the predicted weight is calculated as

Y = -107 + 1.181(185) = 111.485 = 111.5 kg

But for the p-value,

The p-value for each independent variable tests the null hypothesis that the variable has no correlation with the dependent variable. In other words, there is insufficient evidence to conclude that there is effect at the population level.

If the p-value for a variable is less than your significance level, your sample data provide enough evidence to reject the null hypothesis for the entire population. Your data favor the hypothesis that there is a non-zero correlation.

On the other hand, a p-value that is greater than the significance level indicates that there is insufficient evidence in your sample to conclude that a non-zero correlation exists, especially at population level.

Here, the p-value = 0.285, significance level = 0.05, p-value > significance level, hence, the predicted weight might not hold true at the population level though.

Hope this Helps!!!

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step-by-step explanati∵∵∴∴on: