Exam 7: Linear Regression

Listed below is a company's sales in the period 2000 to 2011 along with the national income of the country, where the business is set up. Year National Income (in millions of dollars) Company's sales (in thousands of dollars) 2000 305 470 2001 316 485 2002 358 499 2003 350 515 2004 375 532 2005 392 532 2006 400 556 2007 398 576 2008 430 583 2009 456 587 2010 578 601 2011 498 605 a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between the National Income and the Company's sales in the period 2000 to 2011? b. Use the data to develop an estimated regression equation that could be used to estimate the company's sales based on the national income. What is the estimated regression model?

In a linear regression model, the variable that is being predicted or explained is known as _____________. It is denoted by y and is often referred to as the response variable.

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 employees is selected and the data is given below. $\begin{array}{|c|c|c|c|}\hline\begin{array}{c}\text { Education (No. of } \\\text { years) }\end{array} & \begin{array}{c}\text { Length of tenure in } \\\text { current employment } \\\text { (No. of years) }\end{array} & \text { Age (No. of years) } & \text { Annual income (\$) } \\\hline 17 & 8 & 40 & 124,000 \\\hline 12 & 12 & 41 & 30,000 \\\hline 20 & 9 & 44 & 193,000 \\\hline 14 & 4 & 42 & 88,000 \\\hline 12 & 1 & 19 & 27,000 \\\hline 14 & 9 & 28 & 43,000 \\\hline 12 & 8 & 43 & 96,000 \\\hline 18 & 10 & 37 & 110,000 \\\hline 16 & 12 & 36 & 88,000 \\\hline 11 & 7 & 39 & 36,000 \\\hline 16 & 14 & 36 & 81,000 \\\hline 12 & 4 & 22 & 38,000 \\\hline 16 & 17 & 45 & 140,000 \\\hline 13 & 7 & 42 & 11,000 \\\hline 11 & 6 & 18 & 21,000 \\\hline 20 & 4 & 40 & 151,000 \\\hline 19 & 7 & 35 & 124,000 \\\hline 16 & 12 & 38 & 48,000 \\\hline 12 & 2 & 19 & 26,000 \\\hline 10 & 6 &44& 124,000 \\\hline\end{array}$ a. Check if the F test leads to conclude that an overall regression relationship exists. If yes, use the t test to determine the significance of each independent variable. What is the conclusion for each test at the 0.05 level of significance? b. Remove all independent variables that are not significant at the 0.05 level of significance from the estimated regression equation. What is your estimated regression equation in this case?

_____________ refers to the scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable.

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

The coefficient of determination

What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89?

The process of making conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as

Listed below is a company's sales in the period 2000 to 2011 along with the national income of the country, where the business is set up. Y ear National Income (in millions of dollars) Company's sales (in thousands of dollars) 2000 305 470 2001 316 485 2002 358 499 2003 350 515 2004 375 532 2005 392 532 2006 400 556 2007 398 576 2008 430 583 2009 456 587 2010 578 601 2011 498 605 Test whether each of the regression parameters β₀ and β₁ is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters?

In the graph of the simple linear regression equation, the parameter $B _ { 0 }$ represents the ___________ of the regression line.

A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called