Asked by Jaime Alexander on May 31, 2024
Verified
Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. 
= 12 + 1.8x
N = 17
SSR = 225
SSE = 75
Sb1 = .2683
The t statistic for testing the significance of the slope is
A) 1.80.
B) 1.96.
C) 6.71.
D) .56.
Regression Analysis
A statistical method for estimating the relationships among variables, often for predicting a dependent variable based on one or more independent variables.
Significance
The degree to which a result, difference, or relationship in data is not likely to occur randomly or by chance but rather is likely to be true.
Slope
The measure of the steepness or angle of a line, indicating the rate at which one variable changes with respect to another.
- Interpret the significance of regression coefficients using the t statistic.
Verified Answer
t = b / (SEb)
where b is the estimated slope coefficient, and SEb is the standard error of the slope coefficient.
From the given information, b = 1.8 and Sb1 = .2683. Therefore, SEb = .2683 / sqrt(17) ≈ .065.
Substituting these values into the formula for t, we get:
t = 1.8 / .065 ≈ 27.69
This t statistic is much larger than the critical t-value for a two-tailed test with 15 degrees of freedom and a significance level of .05, which is approximately 2.13. Therefore, we can reject the null hypothesis that the slope is equal to zero and conclude that there is a significant linear relationship between advertising and sales. The correct choice is C.
Learning Objectives
- Interpret the significance of regression coefficients using the t statistic.
Related questions
A Researcher Conducts a Study Measuring 10 People Before and ...
What Is the Value of X D for the Following Set ...
A Researcher Conducted an Analysis That Supported the Research Hypothesis ...
An Actuary Wanted to Develop a Model to Predict How ...
In Testing the Mean of a Sample, Calculating a Negative ...