Question

1. Given that BMI = 29.578 - 0.655 PA, where PA is a measure for Physical Activity given by thousands of steps per day:

What is the predicted BMI for a woman who averages 9500 steps per day? (report to one decimal place)

2. Given what you found in the previous question 5: If an observed BMI at x=9.5 were 24.3, what would be the residual? (report to 1 decimal place)

3. Given that:

n =20

y = 28.5 + 1.4x

SE_b1 = 0.65

What is the test statistic? (report to 2 decimal places)

4. Given the t-statistic you found in question 7, would you reject the null hypothesis at the 5% level using a two-sided alternative? (you will need to find your p-value!)

YES

NO

Answer 1

given that

BMI = 29.578 - 0.655 PA

where PA is a measure for Physical Activity given by thousands of steps per day

1)

Here no.of steps =9500 that is 9.5k so PA =9.5 hence

BMI =29.578 - 0.655 PA=29.578-0.655*9.5 =23.3555

2)

residual =Predicted Value -Actual Value =23.3555-24.3=-0.9445

3)

Here

n=20 and we have two parameters constant and slope hence

DF=n-2=20-2=18

we have to test that

here observed Beta =b1=1.4

so

test statistics is given by

t have DF=n-2=20-2=18

4)

since test is two tailed so

P-Value =2*P(t>2.15) =2*0.0227 =0.0454

Since P-Value is less than level of significance (0.05) Hence we reject H0 Hence

YES