A manager of a local retail store analyzes the relationship between advertising and sales by reviewing the store’s data for the previous six months. She computes the correlation between sales and advertising spending as 0.90. Select ALL that apply.   a. There is a strong positive linear relationship between sales and advertising.   b. As advertising spending increases sales decrease.   c. As advertising spending increases sales increase.   d. There is a weak positive linear relationship between sales and advertising.

A university would like to examine the linear relationship between a faculty​ member's performance rating​ (measured on a scale of​ 1-20) and his or her annual salary increase. The table to the right shows these data for eight randomly selected faculty members. Complete parts a and b.

Jim and Larry run a soup stand. The data below represents the sales of soup that they had on 8 randomly selected days, along with the high temperature on that day.   a) Create a scatter diagram for this data set and comment on whether there is a positive or negative relationship between these variables.b) Calculate the correlation coefficient between temperature and sales.c) Does a linear relationship exist between these variables? Explain to me why or why not this is the case.d) Using excel, calculate the least squares regression equation for this data set. e) Using your equation, predict the soup sales on a day where the temperature is 29 degrees.f) Interpret the slope of this equation.g) Can we use this data set and regression equation to predict the sales on a day when the average temperature is 102 degrees? Why or why not?h) What is the R-squared for this equation? How do you interpret that R-squared?

An economist wants to determine whether there is a linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. The data are shown in the table below. c. Compute and interpret the correlation coefficient. d. Compute and interpret the coefficient of determination. e. Test for the significance of the linear relationship. Use a 0.05 level of significance. State your conclusion. Hint: Your conclusion is either of the following. • There is a significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. • There is no significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. GDP 1.6 3.6 4.9 1.1 0.9 2.9 2.7 2.3 1.6 1.5 (trillion dollars) Carbon Dioxide Emissions 428.2 828.8 1214.2 444.6 264 415.3 571.8 454.9 358.7 573.5 (millions of metric tons)