Question

In: Statistics and Probability

2. (07.05) Which of the following conditions is/are necessary to justify the use of t procedures...

2.

(07.05)

Which of the following conditions is/are necessary to justify the use of t procedures in a significance test for the slope of a regression line? (4 points)

I. For each given value of x, the values of the response variable y are Normally distributed.
II. For each given value of x, the values of the response variable y are independent.
III. For each given value of x, the standard deviation of y is the same.


I only

II only

III only

I and II only

I, II, and III

3.

(07.05)

A researcher wants to determine whether there is a linear relationship between number of rom-com movies and engagements. The table displays a partial computer printout of the regression analysis and is based on a sample of eight subjects.

Predictor Coeff St. Dev t Ratio p-Value
Constant 4.35744984 2.385747738 5.7382918 0.00375268
Rom-com movies 1.34457321 0.526645738


What is the value of the t-test statistic for H0: β = 0? (4 points)

0.004

5.74

−5.74

−2.55

2.55

4.

(07.05)

Researchers are conducting a study in an attempt to establish a linear relationship between the number of online keyboard lesson videos and the number of keyboard sales. A computer output for regression is shown and is based on a sample of eight observations.

Predictor Coeff St. Dev t Ratio p-Value
Constant -4.19411878 7.812571764 -0.53684227 0.601188456
Keyboard Video Views 0.301433595 0.032631691 9.237449496 8.37927E-07


What represents the 98% confidence interval for the slope of the regression line? (4 points)

0.3014 ± 9.237(0.0326)

0.3014 ± 9.237(7.8126)

0.3014 ± 3.143(0.0326)

0.3014 ± 3.143(7.8126)

0.3014 ± 0.537(0.6012)

5.

(07.05)

Researchers pose the question: Can shirt size be predicted from a man's height? A random sample of 15 males and their shirt size versus height (in inches) gives the regression results shown in the table.

Predictor Coeff SE Coeff t Ratio p-Value
Constant -48.81 30.57 -1.60 0.128
Height 0.3736 0.1898 1.97 0.065
S = 4.46720 R-Sq. = 17.7%

R-Sq. (adj) = 13.1%



Is there statistical evidence of a linear relationship between shirt size and height? (4 points)

No, because r2, the coefficient of determination, is too small

No, because 0.128 is above any reasonable significance level

Yes, because, by any reasonable observation, taller men tend to have a larger shirt size

Yes, because the slope is positive

Yes, there is evidence at the 10% significance level, but not at the 5% level

Solutions

Expert Solution

orchestra answered 2 years ago
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