Question

Question 3: Consider 4 values for sales in RONA and renovation investment Consider sales as the response variable): Sales ($M) 0.5 2 1.5 5 Renovation investment ($M) 2 3 5 8 a) Calculate variance and standard deviation for each variable. b) Calculate correlation coefficient. c) Draw a Scatterplot for these variables. Do you think if we can develop a linear model for this relationship? Why? d) Develop a linear regression model to predict sales based on renovation investment. e) Check the credibility of your linear model based on R-squared (R) and the scatterplot of residuals. Calculate R-squared (R?) with two methods. Is your model credible? Why? f) How much is your sales prediction for the manager of RONA if according to statistics CANADA renovation investment in the next year is estimated to be 9.2 $M?

Answer 1

In this high school mathematics question, we calculate the variance and standard deviation for each variable, find the correlation coefficient, create a scatterplot, develop a linear regression model, evaluate its credibility through R-squared, and predict sales based on a new renovation investment value.

Step-by-step explanation:

a) Variance and Standard Deviation

To calculate the variance and standard deviation for each variable, follow these steps:

1. Calculate the mean of the variable.
2. Subtract the mean from each value, and square the result.
3. Calculate the average of the squared differences.
4. Take the square root of the average to find the standard deviation.

For the Sales variable, the variance is 4.25 and the standard deviation is approximately 2.06. For the Renovation Investment variable, the variance is 4.5 and the standard deviation is approximately 2.12.

b) Correlation Coefficient

The correlation coefficient measures the strength and direction of the relationship between two variables. To calculate the correlation coefficient: