**STAT20029 (T2,2020) Questions:**

**Week 11-Chapter 13**

**Activity 11.1**

Activity 11.1: The scatter diagram below plots grip strength (Ratings) against arm strength to push (Arm). Identify if the plot indicates positive, zero, or negative correlation between the variables. (Mere statement will do, there is no need to comment or calculate.)

**Activity 11.2**

Activity 11.2: The following data show the amount of money(in millions of dollars) spent on Research and development by a company and the resulting Sales (in millions of dollars)

(a) Produce a scatterplot of the data. Does there appear to be any correlation between exam score and sales? Explain.

(b) Compute the correlation coefficient. Comment on this value.

**Activity 11.3**

Activity 11.3: A group of 5 persons each weighing 90 kg were selected. They were given an exercise routine of running a certain distance each week while maintaining similar diet habits. After one-year their weights were recorded against the distance they were assigned to run. The table below shows the weights of individuals (Y in kg) against the distance that person was assigned to run each week (X in km). Calculate r and comment on the strength of the relationship.

**Activity 11.4**

The following data shows the amount of money (in millions of dollars) spent on Research and Development by a company and the resulting Sales (in millions of dollars).

(a)Find the estimated regression equation of Y on X.

(b) If R&D = $2.5m then estimate the value of sales.

(c)For example, if R&D = $10.5m, can you predict the sales?

**Practice Problem 13.4**

PP13.4: Investment analysts generally believe that the price of fixed rate bonds is inversely related to the prime interest rate for loans; that is, bonds perform well when lending rates are down and perform poorly when interest rates are up. Can the bond rate be predicted by the prime interest rate? Construct a least squares regression line to predict bond rates using the prime interest rate.

**Activity 11.5**

Activity 11.5: A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small towns and offers the candy bar at different prices. Using candy bar sales as the dependent variable, determine a simple linear regression equation for the data.

**Activity 11.6**

**Activity 11.6: **A professor wants to use the number of hours a student studies for a final (X) to predict the final examination score (Y). The previous semester result gave the following result:

Interpret the coefficient and intercept.

**Activity 11.7**

**Activity 11.7: **The management of a chain electronic store would like to develop a model for predicting the weekly sales for individual stores based on the number of customers who made purchases. Using sales as the dependent variable, determine a simple linear regression equation for the data.

**Activity 11.8**

**Activity 11.8: **Data were collected for six cities on their populations (in millions) and the market value of the cities’ real estate (in billions of dollars), as given in the table:

(a) Find the sample correlation between population and real estate value.

(b) Calculate coefficient of determination and interpret its value.

**Activity 11.9**

**Activity 11.9: **A homebuilders association lobbying for various home subsidy programs argued that, during periods of high interest rates the number of building permits issued decreased dramatically, which in turn reduced the availability of a new housing. The annualized interest rate on housing loans varied from 7% to 13.5%. A summary of the collected two variable data (subsequently sampled over 25 years) of annualized interest rates (X) and the new house approvals (Y) in thousands is provided:

(a)Find the least squares regression line equation that expresses the number of building permits Y issued as a function of annualized interest rate X on home loan.

(b) Calculate the Coefficient of Determination. Comment on the value.

**Practice Problem 13.14**

**PP13.14: **Graph the following residuals and indicate which of the assumptions underlying regression analysis appear to be violated.

**Practice Problem 13.15**

PP13.15: Study the following residuals graph for a simple regression analysis. Comment on the residual evidence of lack of compliance with the regression assumptions.

**Activity 11.10**

Activity 11.10: Identify what the following scatterplot of residuals from a simple linear regression analysis indicates. Y axis gives the residual values and X axis the values of the independent variable.

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