Math Problem Statement

A random sample of 148 artworks created within the last three years and sold at auction has been selected to study art auction price and prior exhibition. Some of the variables recorded for each artwork are listed below.

Variable Description subid Subject ID medium type of artwork exhibWeeks the number of weeks the artwork was exhibited before the auction price sale price (in thousands)

A simple linear regression is run to answer the research question, ’What is the relation between sale price (in thousands) and the number of weeks the artwork was exhibited before the auction?’ The results of the analysis are reported below:

        Estimate Std. Error t value Pr(>|t|)

(Intercept) 35.7358 2.0599 17.3486 0 exhibWeeks 0.7636 0.0547 13.9596 0 Address the following questions, assuming as necessary that all test assumptions are verified.

What is the null hypothesis? Choose one among the following options: a. The slope of the regression line is either positive or negative b. There is a significant relation, linear or non-linear, between the two variables c. The slope of the regression line is significantly different from zero d. The slope of the regression line is zero e. There is no relation whatsoever, linear or non-linear, between the two variables f. The relation between the two variables is linear Answer 1 Question 1 From the test statistic as reported above, we can conclude that the estimated value of the slope is: Answer 2 Question 1 From the p-value as reported above, we can conclude that the decision of the test is: Answer 3 Question 1 What is the conclusion of the test?

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Hypothesis Testing
Statistical Inference

Formulas

Linear regression formula: y = β0 + β1x
t-value formula: t = (Estimate - Hypothesized Value) / Std. Error
Hypothesis test for regression: H0: β1 = 0, Ha: β1 ≠ 0

Theorems

Central Limit Theorem
t-Distribution

Suitable Grade Level

Undergraduate Level (Statistics or Data Analysis)