Problem $2$: Analyzing the Relationship Between Employee Satisfaction and

Productivity

A company wants to assess how employee satisfaction affects their productivity. They have

collected data from $30$ departments and measured both employee satisfaction scores and

productivity $($measured as output per hour worked$).$ They want to use linear regression to

understand whether higher employee satisfaction correlates with increased productivity.

Questions:

$1.$ Fit a linear regression model to predict productivity based on employee satisfaction.

What is the regression equation?

$2.$ Interpret the slope of the regression line in the context of the business. What does it tell

you about the relationship between satisfaction and productivity?

$3.$ Interpret the intercept of the regression line. What does it mean in the context of this

analysis?

$4.$ Are the independent variables significant at the $5\%$ level of significance?

$5.$ Predict the productivity of a department where the satisfaction score is $92.$

$6.$ Assess the strength of the relationship between employee satisfaction and productivity.

What metric would you use, and what does it tell you?

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline Department & Satisfaction Score $(0-100)$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Productivity $\backslash \backslash$

$($Output per Hour$)$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $1$ & $78$ & $16\backslash \backslash$

$\backslash$hline $2$ & $88$ & $15\backslash \backslash$

$\backslash$hline $3$ & $74$ & $15\backslash \backslash$

$\backslash$hline $4$ & $81$ & $17\backslash \backslash$

$\backslash$hline $5$ & $91$ & $14\backslash \backslash$

$\backslash$hline $6$ & $96$ & $19\backslash \backslash$

$\backslash$hline $7$ & $65$ & $9\backslash \backslash$

$\backslash$hline $8$ & $75$ & $14\backslash \backslash$

$\backslash$hline $9$ & $90$ & $17\backslash \backslash$

$\backslash$hline $10$ & $82$ & $18\backslash \backslash$

$\backslash$hline $11$ & $92$ & $16\backslash \backslash$

$\backslash$hline $12$ & $67$ & $13\backslash \backslash$

$\backslash$hline $13$ & $93$ & $14\backslash \backslash$

$\backslash$hline $14$ & $90$ & $19\backslash \backslash$

$\backslash$hline $15$ & $70$ & $17\backslash \backslash$

$\backslash$hline $16$ & $83$ & $20\backslash \backslash$

$\backslash$hline $17$ & $80$ & $13\backslash \backslash$

$\backslash$hline $18$ & $85$ & $19\backslash \backslash$

$\backslash$hline $19$ & $87$ & $17\backslash \backslash$

$\backslash$hline $20$ & $89$ & $15\backslash \backslash$

$\backslash$hline $21$ & $97$ & $20\backslash \backslash$

$\backslash$hline $22$ & $100$ & $22\backslash \backslash$

$\backslash$hline $23$ & $94$ & $20\backslash \backslash$

$\backslash$hline $24$ & $99$ & $16\backslash \backslash$

$\backslash$hline $25$ & $98$ & $22\backslash \backslash$

$\backslash$hline $26$ & $84$ & $16\backslash \backslash$

$\backslash$hline $27$ & $95$ & $16\backslash \backslash$

$\backslash$hline $28$ & $76$ & $15\backslash \backslash$

$\backslash$hline $29$ & $86$ & $17\backslash \backslash$

$\backslash$hline $30$ & $72$ & $14\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$