The manager of a furniture factory that operates a morning and evening shift seven days a week wants to forecast the number of chairs its factory workers will produce on a given day and shift. The production manager gathers chair production data from the factory and lists whether the production day was a weekday or a weekend (i.e., Saturday or Sunday), and whether the shift was in the morning or evening. Create a regression model to analyze the relationship between the number of chairs produced, whether a day was a weekday or weekend, and whether the shift was in the morning or evening. Be sure to include the residuals and residual plots in your analysis.

From the details, note that the manager of a furniture factory that operates a morning and evening shifts seven days a week wants to forecast the number of chairs to be produced on a given day and shift by its factory employees.

Consider Y is the vector reflecting the number of chairs the factory produces for its employees.

The independent variables are:

[tex]x_{1i}[/tex] = 1 Weekday (Mon to Fri)

0 Weekend (Sat and Sun)

[tex]x_{2i}[/tex] = 1 Morning Shift

0 Evening shift.

Observe that the regression line is as follows from the regression output given in the problem:

Ŷ = 405.58 + 70.97 * Weekday + 47.85 * Shift.

Calculate the number of chairs during the evening shift which will be generated on a Thursday.

For this problem, [tex]x_{1} = 1[/tex] because it's weekday and [tex]x_{2} = 0[/tex] because it's a shift from the evening.

Ŷ = 405.58 + 70.97 * Weekday + 47.85 * Shift.

= 405.58 + 70.97 * (1) + 47.85 * (0)

= 405.58 + 70.97 + 0

= 476.55

= 477

Thus, the number of chairs that will be generated during the evening shift on Thursday will be 477.