A manager at a roadside cafe is concerned that the weak economic environment has caused a decline in sales. To offset the decline in sales, the manager has pursued a strong advertising campaign (billboards up and down the road). She believes advertising expenditures have a positive influence on sales. To support her claim, the manager estimates the following linear regression model: Sales = Bo + B1Unemployment + B2Advertising + E. A portion of the regression results is shown in the accompanying table. ANOVA df MS F Significance F 0.003 Regression 2 72.6374 36.3187 9.674 Residual 14 58.0438 4.1460 Total 16 130.681 Standard Coefficients Error t Stat p-Value Intercept 17.5060 3.9817 4.397 0.007 Unemployment Advertising -0.6879 0.2997 -2.296 0.038 0.0266 0.0068 3.932 0.022 What is the value of the test statistic regarding whether the predictor variables jointly influence sales (round to 3 decimal places)? At the 5% significance level, do the predictor variables jointly influence sales? (Y/N) Is Advertising negatively related with sales? (Y/N) Are both Unemployment and Advertising statistically significant in this model? (Y/N) What is most likely wrong with this model?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![A manager at a roadside cafe is concerned that the weak economic environment has caused a decline in sales. To offset the decline in sales, the manager has pursued a
strong advertising campaign (billboards up and down the road). She believes advertising expenditures have a positive influence on sales. To support her claim, the
manager estimates the following linear regression model: Sales = Bo + B1Unemployment + B2Advertising + E. A portion of the regression results is shown in the
accompanying table.
Significance F
0.003
ANOVA
df
MS
F
36.3187
Regression
Residual
2
72.6374
9.674
14
58.0438
4.1460
Total
16
130,681
Standard
Error
t Stat
p-Value
0.007
Coefficients
17.5060
3.9817
Intercept
Unemployment
Advertising
4.397
-0.6879
0.2997
-2.296
0.038
0.0266
0.0068
3.932
0.022
What is the value of the test statistic regarding whether the predictor variables jointly influence sales (round to 3 decimal places)?
At the 5% significance level, do the predictor variables jointly influence sales? (Y/N)
Is Advertising negatively related with sales? (Y/N)
Are both Unemployment and Advertising statistically significant in this model? (Y/N)
What is most likely wrong with this model?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5b2b20d-049f-4dcf-af25-64fd11186c52%2F8c26e210-35e8-4dd9-a805-954dc6a1ba39%2Fuomxjn6_processed.png&w=3840&q=75)
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