Given the linear regression equation:

y = 1.6 + 3.5x1 - 7.9x2 +2.0x3

a. Which variable is the response variable? How many explanatory variables are there?
b. If x1 = 2, x2 = 1 and x3 = 5, what is the predicted value for y?
c. Supposed the n = 12 data points were used to construct the given regression equation above, and that the standard error for the coefficient x1 is 0.419. Construct a 90% confidence interval for the coefficient of x1.
d. Using the information from part c and 5% level of significance, test the claim that the coefficient of x1 is different from 0. What does your conclusion mean in relation to x1 predicting y?

a. y is the response variable. There are 3 explanatory variables, namely x1, x2 and x3.

b. y = 1.6 + 3.5 x 2 - 7.9 x 1 + 2 x 5 = 10.7

c. 90% confidence interval for the coefficient of x1 = (2.721, 4.279)

d. The claim is true. x1 has predictability towards y.

Step-by-step explanation:

c. Use the following four-step approach to construct a confidence interval.

- Identify a sample statistic. From the regression equation, we see that the coefficient of x1 is 3.5

- Select a confidence level. We are working with a 90% confidence level.

- Find the margin of error

•Find standard error for the coefficient of x1. The standard error is given as 0.419

•Find critical value. The critical value is a t score with degrees of freedom equal to n - k (n= number of data points, k = number of parameters). To find the critical value, we take these steps.

oCompute alpha (α):

α = 1 - (confidence level / 100)

α = 1 - 90/100 = 0.1

oFind the critical probability (p*):

p* = 1 - α/2 = 1 - 0.1/2 = 0.95

oFind the degrees of freedom (df):

df = n - k = 12 - 4 = 8.

oThe critical value is the t statistic having 8 degrees of freedom and a cumulative probability equal to 0.95. From the t Distribution Calculator, we find that the critical value is 1.86.

•Compute margin of error (ME):

ME = critical value * standard error

ME = 1.86 * 0.419 = 0.779

Specify the confidence interval. The range of the confidence interval is defined by the sample statistic + margin of error. And the uncertainty is denoted by the confidence level.

Therefore, the 90% confidence interval for the coefficient of x1 is 3.5 ± 0.779, which is 2.721 to 4.279 .

d. 5% level of significance is conversely translates to a 95% level of confidence. Using the same approach, we identify the 95% confidence interval for the coefficient of x1 is 3.5 ± 0.966, which is 2.534 to 4.466 .

0 falls out of the confidence interval, therefore the claim that the coefficient of x1 is different from 0. It means x1 has predictability towards y.

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: